Stat Assistant Professor

I don't think domestic students are at any disadvantage for Masters programs in Statistics (and for *PhD* programs in Stat/Biostat, being domestic is actually an advantage if anything, because it's a little bit less competitive vs. for international students, NIH trainee grants can only go to U.S. citizens/permanent residents, etc.). MS programs in Stat aren't typically funded so they will tend to admit most people -- international OR domestic -- who meet the minimum program requirements for GPA, GRE Q score, and coursework (usually just Calculus I-III and Linear Algebra).
I think it's just that more international students are interested in pursuing advanced degrees in Statistics (similarly with other fields like Computer Science). For that reason, you'll see more international students in most Statistics grad programs. 

It will vary by department, when you take the quals etc. In my case it was:
After year 1: research project with a small stipend. Basically to get you used to doing research, reading journal articles etc. I read several articles of interest, reproduced the results while at the same time teaching myself to write code. Some students already entered the PhD program with an advisor in mind so they basically jumped right into research.  TA-ships were available for a limited number of students but we all got a small stipend ($2500/summer) to help keep us afloat. Being a summer TA would've doubled summer funding to $5000.
After year 2: prepare for quals which are taken in August. Do research or a consulting project. Again, small stipend ($2500) with TA-ships available (another $2,500) if desired for a limited number of students (this was highly discouraged for those studying for quals).
After year 3: start getting serious about research and preparing for the prelim oral exam. Do research. TA-ships ($2,500/summer) and grad instructor positions ($5,000/summer) available again. Some students did an industry internship this summer as well.
After year 4: By the end of year 4 you should've finish your prelim oral exam. Work on dissertation/research and be a summer TA or grad instructor. Some industry-bound students also did an internship this year.

I am not sure what "Applicable Algebra" is. Is this a proof-based linear algebra class or abstract algebra? I think analysis and maybe advanced linear algebra should be sufficient for the Biostat programs on your list. I think you are in good shape for Biostatistics programs. Some of the top Statistics programs (Chicago, Columbia, Berkeley) may have a preference for students who have deeper math backgrounds, so it's hard to gouge your chances to the stats programs on your list -- on the other hand, you have a strong pedigree and your research experience is solid, so I'm not sure how much adcoms will take that into account. If I were you, I would apply to more top 20 schools for Statistics, like University of Minnesota, NCSU, TAMU. 
If you haven't taken real analysis or abstract algebra before, then I don't anticipate that you would be able to score high on the Math Subject GRE. And even those who have taken those classes need to study a lot to do well on the Subject test. Therefore, it may not be worth your time and effort. Doing well on this test may help for Columbia, UChicago, and Yale, but as far as I know, it isn't required at any school except for Stanford. And a high score on the subject test isn't really a substitute for having taken the classes and getting good grades in them.

Since you're performing very well academically at an Ivy League School known for slight grade deflation and you have great research experience with some papers in preparation, I think your chances of getting into a top program are quite good. I think you should be able to get into those Biostatistics programs. For Stat, I don't think you need to apply to Northwestern. If you want to add a few "safer" options, I would add Texas A&M, UCLA, and NCSU (these aren't "safe" schools in general, but specifically for your profile, I think that they are very safe bets).
That said, it is worth noting that Columbia Biostatistics is not in the same league as Harvard, UW, JHU, or UNC for BIostat. And some of the programs you have listed are quite different. For instance, Yale S&DS strikes me as quite theoretical, while Columbia Biostat is quite applied. You may want to take stuff like that into account. If you want to do less theoretical stats, then Berkeley Statistics is a good choice (UCB is strong all-around in probability theory, thoeretical stats, and applied stats), and I would also add some schools like University of Washington (they have great faculty in demography and social science stats, for example).

You can look at the program webpages of schools that interest you and see where their alumni have placed. If this info is not available, you can usually get it from the Director or Coordinator of Graduate Studies. PhD programs generally offer funding, but some schools will accept unfunded students too (and that includes ranked programs like Florida State, Arizona State, etc.). The better option is always to go with the *funded* program if you can.
Unranked/lower ranked PhD programs should be fine for either industry or (believe it or not) academia. However, one's chances in academia (for research universities) seems to depend heavily on the PhD advisor and often requires doing a prestigious postdoc with a well-known PI (for example, I know of a few PhD alumni from University of Illinois at Chicago, Baylor University, UC Santa Cruz, and University of Cincinnati who have managed to get tenure-track/tenured jobs in Statistics at Iowa State, Texas A&M, Virginia Tech, and University of Florida). However, those are all good schools even if they are not ranked in USNWR. 
For industry, that doesn't seem to matter all that much (although a well-connected PhD advisor can often help for industry/government/nonacademic positions too). Even without a famous advisor, PhD grads should be able to get good industry jobs, regardless of where they attended. 

I think at UC Berkeley, "lower division" generally means the Calculus sequence and intro linear algebra. Anything after that is considered an "upper division" class. So it's not so much what year you took the upper division classes, but any classes that are more advanced than Calculus and a first course in linear algebra. See here: 
https://statistics.berkeley.edu/programs/undergrad/major#Prereqs
https://math.berkeley.edu/programs/undergraduate/major/applied
https://math.berkeley.edu/programs/undergraduate/major/pure
 
If you took any advanced math classes in your freshman/sophomore year *after* Calculus and introductory linear algebra class, then I would include those on your list. Likewise, if you took any statistics courses beyond the introductory survey course (which typically covers descriptive statistics through two-sample hypothesis tests), you could include those.

At my PhD program, we had to take 2 full years of required classes, including two semesters of measure theoretic probability, and each of the first two years was followed by a 4-hour written exam. Then you had to take 4 additional electives, so most students didn't finish classes until their third (or fourth year, if they really dragged out the requirement). But it was typically 3 classes a semester for the first two years, and then 1-2 classes per semester after that.
For this reason, the overwhelming majority of students in my program didn't start research until the summer after their second year (one exceptional student started it in his first year, because he did an independent study and actually got publishable results just from that). Most people started after their second year and still graduated within 5 years, so it didn't seem as though the coursework really put anyone "behind." This past year, only one of the fifth year students graduated, while the rest of that cohort staying for a sixth year --  however, that was mainly because of the disruption caused by COVID, the temporary suspension on H1-B visas, etc. I'm sure under "normal" circumstances, most of the 5th year students would have graduated.
If excessive coursework is a potential concern, you could ask the graduate coordinator what the mean time for completion is. If the average completion time still seems reasonable to you, then I wouldn't be too deterred by the coursework.  
As for the value of the coursework... I certainly don't use everything from what I learned (rather, bits and pieces here and there). But I think that it did help indirectly and made me more mathematically mature. I also gained a greater appreciation for probability theory later on when I was exploring the more theoretical aspects of my research, even though I found it very abstract and difficult when I was taking it.

I would make sure to follow each graduate school's application instructions to a tee. If only three letters are requested, then only send three. If the applications allow "up to four," then a fourth one is probably okay.

I think you should have an above average shot at NCSU and Duke. After all, you did go to a top liberal arts college and did pretty well in the math and stats classes you did take. Your profile is by no means a "shoe-in" at these places, but I think that if you can get excellent letters of recommendation, I wouldn't discount your chances at either of these schools. Your profile reminds me: there is an outstanding statistics researcher James Johndrow (now an Assistant Professor at Penn Wharton) who got his PhD in Statistical Science from Duke even though his undergrad degree was in Chemistry (also obtained from a top liberal arts college). And I also know of a young woman whose Bachelor's is in Psychology/Pre-med from Columbia but she also got her PhD in Statistics from NCSU (now a postdoc at Columbia). I think that Duke and NCSU are more open to accepting applicants from "lighter" math backgrounds and different majors than other places -- I know of at least a couple students/alumni from NCSU and Duke Statistics who did not have extensive math backgrounds. However, they did come from strong pedigrees, so your chances may be inversely proportional to how prestigious your undergrad is (that is, you can possibly get away with a lighter math background if your undergrad institution is very prestigious. But if you went to an unknown school, then you need to have very strong performance in math classes to be competitive).
However, UPenn Wharton, CMU, and Columbia may be tough for you to break though without a lot more math, and I would recommend that you apply to a wide range of PhD programs, like the other posters have suggested. I also think you can definitely get into a top 10 Biostats PhD program, no question, if you think that this aligns better with your interests than traditional Statistics programs.

Definitely not an issue. 

Given your academic performance and your pedigree, your profile looks very strong. Even if you didn't get additional research experience, I would anticipate that you would be able to get into some very good PhD programs -- you have a great shot at programs in the top 15. With great letters of recommendation, you should be in very good shape.
Re: research. Adcoms probably won't expect most undergrads to have research in theoretical statistics (it happens occasionally, but is quite rare). However, your research experience with the Department of Communication at a peer university is definitely a plus. The main benefit of research experience is getting good letters of recommendation. Therefore, it might be beneficial for you to get involved in some applied statistics research or interdisciplinary research in related fields, e.g. epidemiology, public health, etc. That way, you can obtain a good letter of recommendation from a research supervisor. If you can get a good letter from a professor who supervised your work on applications of ML and statistics to political science, then you might not need to do other research. 

If your undergrad was from an elite school like HKUST, the Chinese University of Hong Kong, or University of Hong Kong (these three schools in Hong Kong enjoy very strong international reputation, and they've sent their graduates to top Stat PhD programs like Columbia, University of Washington, etc.), then I think you shuld be in very good shape to get into top Statistics PhD programs. That, plus your Masters degree at an elite school, should make you competitive.
You can certainly afford to aim a lot higher than UVA, Georgetown (which is an excellent school but less well-known for stat/math), or UMBC. I think your chances at Duke and UNC are above average, and you should be able to safely get into Penn State. If you are more geographically flexible, you could apply to more top stat top 20 stat PhD programs. But if you really are geographically constrained to the mid-Atlantic region, I think you should also apply to:
North Carolina State University Department of Statistics (I think you would get in there) Johns Hopkins Department of Applied Math and Statistics JHU Biostatistics  University of Maryland AMSC (they're not ranked in Statistics because statistics is part of their math department, rather than its standalone department -- but UMD has a very strong math department, ranked #22 by USNWR).

The experimental physics professor seems like he would be able to write a more meaningful letter for you.

I'm not saying prestige doesn't matter at all. It can make a difference, and there are many benefits to going to a top school (like a greater number of "superstars" and professors who are internationally recognized, possibly more job connections, etc.). But at the end of the day, you make your own success. Above all else, departments want to hire somebody who has a good record of scholarship and the *future potential* to continue producing quality research after they're hired. And you can accomplish that with a PhD from any reputable school (though it might be easier to build a track record at a top school). A hiring committee is *not* going to be like, "This person has two papers in JASA/Biometrika/Annals/JRSS and seven total papers, but their PhD is from the University of Illinois at Chicago? We won't consider them at all."  
 

Right, the PhD advisor and the research area both matter a great deal. For example, it is typically going to be harder for a probabilitist to get an academic job than a statistician, even if the probabilitist went to a "top" school (the demand isn't as high, so if you do go into probability theory, you have to be *really, really* good at it to land an academic job at a research university). There are also some unranked programs that have good people, like University of Cincinnati and University of California-Santa Cruz where there are/were a lot of good professors like Bruno Sanso and Abel Rodriguez (Rodriguez recently moved to UW Statistics) who have a strong track record of academic placements.
I just meant to convey that success is not determined only by the prestige of PhD institution (although that does help), but also by a proven record of good scholarship, PhD advisor, postdoctoral experience, research area, etc.

If you go to a lower-ranked department, make sure there are people who are actively publishing in top statistics journals (not from 20-30 years ago) and you can be successful.  I purposefully chose an unranked department over a top one because I knew there were people I wanted to work with. Just a warning that the UIC story above is an extreme outlier -- Ryan Martin was briefly a professor at UIC before moving to NCSU (a top department) and he is probably one of the most prolific young statisticians, and the Iowa State prof is one of his old students.  It is unlikely there are any advisors like him at non-top-50 departments today.

Given your profile, the advice I gave in the other post remains the same. I think you need to focus on schools ranked lower than USWNR top 60 and also apply to some unranked PhD programs as well. If your ultimate goal is industry, then that is not a problem at all.
If your ultimate goal is academia, I would like to point out that there was one person whose PhD was from the University of Illinois at Chicago (an unranked program -- and they combine math, statistics, and computer science all in the same department) who got an Assistant Professor job at the Iowa State University Department of Statistics this past year, which is a really good Statistics department. And the school where I got my PhD (ranked ~40) hired someone whose PhD was from University of Cincinnatti a couple years ago, and he is really killing it. This scenario may not be "common," but it goes to show that your record of achievement is what really matters above all else.
In addition, most primarily undergrad institutions outside of the very elite ones (i.e. colleges without PhD programs) care even less about PhD granting institution -- passion for teaching and interdisciplinary research with undergrads is what matters most. So if you are open to jobs at PUIs, that is also something to consider.

I think your job resume plus being sure to include any research experience would be fine. I wouldn't overthink this.  Mine was pretty barebones. 

Yes, that Stats 300C class at Stanford is one possibility. I would say that a PhD-level advanced inference class should focus less on topics like UMVUE, Neyman-Pearson Lemma, admissibility, etc., but more on stuff like theory for shrinkage methods, convex/nonconvex optimization, reproducing kernel Hilbert spaces, resampling methods, etc. That's because the latter topics are more of current interest and are active areas of research.

Yes, that Stats 300C class at Stanford is one possibility. I would say that a PhD-level advanced inference class should focus less on topics like UMVUE, Neyman-Pearson Lemma, admissibility, etc., but more on stuff like theory for shrinkage methods, convex/nonconvex optimization, reproducing kernel Hilbert spaces, resampling methods, etc. That's because the latter topics are more of current interest and are active areas of research.

Yes, that Stats 300C class at Stanford is one possibility. I would say that a PhD-level advanced inference class should focus less on topics like UMVUE, Neyman-Pearson Lemma, admissibility, etc., but more on stuff like theory for shrinkage methods, convex/nonconvex optimization, reproducing kernel Hilbert spaces, resampling methods, etc. That's because the latter topics are more of current interest and are active areas of research.

The most "typical" required coursework seems to be:
2 semesters of Casella & Berger mathematical statistics  2 semesters of applied statistics (based on the book "Applied Linear Statistics" by Kutner et al.) 1 semester of statistical computing 1 or 2 semesters of measure theoretic probability 1 semester of linear models theory 1 or 2 semesters of advanced statistical inference Some elite PhD programs like Stanford and UPenn Wharton skip the first two sequences above because the students they admit are fairly advanced already. 
Anyway: my opinion is that the typical first-year courses are fine for the most part, though they certainly should be updated to incorporate current research topics. If an entering student has not already had much exposure to statistics at the graduate level, then I think it's fine to teach the topics like linear regression, ANOVA, GLM/categorical data analysis, and theory of sufficient statistics, point estimation, hypothesis testing, etc. in detail... though I definitely agree that some of their curricula should be updated. For example, at my PhD program, an entire semester was devoted to different ANOVA/ANCOVA models, including things like split plot design, etc. That seemed a bit excessive to me -- usually, you only need to go over a couple of ANOVA models in detail to get the general gist. So if I were on the PhD curriculum committee, I would probably "modernize" the applied stats sequence (and the statistical computing class) to spend less time on design of experiments and include more modern topics.
Additionally, the advanced statistical inference courses (i.e. the theoretical statistics course(s) you take in the second or third year) at many programs do seem to focus on some topics that are dated. For example, at some schools, you learn to cross every "t" and dot every "i" for "classical" topics like UMP tests, UMVUE, equivariance, likelihood principle, etc., which isn't necessarily helpful for modern statistics research. 
I would probably repurpose the advanced statistical inference classes to cover more 'modern' statistical theory like multiple testing/knock-offs, RKHS and nonparametric regression, convex/nonconvex optimization for high-dimensional regression, graphical models, etc. 

Yeah, I can't imagine customizing letters of recommendation for every place. I have written a few letters of recommendation and always just sent the same one everywhere.
Even for faculty positions, my letter writers sent exactly the same letters to every place I applied to. I also did not customize the CV, research statement, or teaching statement. I did customize the cover letters, however (just FYI, for anyone who may be interested: the cover letters are especially important for faculty applications to PUIs because they really don't want to hire someone who will jump ship to a research university the second that opportunity arises). Those cover letters took awhile to write, because I spent at least 45 minutes looking through each department's webpages, faculty profiles, course catalogues, etc. 

In my PhD cohort of 9 students who finished the program, there were two of us that got TT positions (one is doing a postdoc now and the other 6 went into industry). Both of us applied to between 50-60 TT positions. Usually people focus their search on either research universities OR on PUIs. Some apply to both, but it's usually tilted more towards one or the other. In our cases, we only applied to jobs at research universities.
The number of TT faculty positions to apply to also depends on your profile. If you have several JASA/AoS/JRSS/Biometrika/Biometrics papers (including the applied stats journals like JASA-Case Studies & Applications or JRSS: Series C), you can afford to be a bit more selective -- but not *too* selective. But if there's a location that you absolutely cannot see yourself living in, you can probably safely exclude it from your list of job applications if your CV is impressive. This isn't the case with pure math, where even a PhD from MIT or Harvard doesn't preclude you from ending up at in a very remote location.  

I often find that the best way to learn a new field/subject is to watch video lectures, read review articles and read select chapters from textbooks. So when I wanted to learn about variational inference, the first thing I did was watch a few video tutorials by David Blei and Tamara Broderick. After establishing this "baseline," I kind of just pick up on things as I go -- i.e. I just read the papers and try to figure out what the authors are doing as I go. This gets easier to do as you gain more experience and as you read more papers (in the beginning, I might annotate the papers a lot more). 
Realistically, when you are doing research, you won't know (or need to know) *everything* there is to know about, say, convex or nonconvex optimization. But you can pick up what it is you need as you go, and if you encounter something you're not familiar with, you get better at knowing WHERE to look and fill in those gaps.