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It might be ok and you can get a sense of the cutoff by checking the Gradcafe result page. GRE Q is usually used as a filter. That said, a high score won't help but a low score will disqualify you. I would say that a >90th percentile on GRE Q won't hurt at any schools.

I would retake it if you have the time. Ideally you should have near perfect score on GRE Q, say 168+. A 164 is not a disaster but it might hurt your chances for top schools.

Only a few top schools recommend/require the test. If the test is cancelled due to the pandemic, I guess they will waive the requirement so I wouldn't worry about it.

UC Davis has a good program and is especially known for research in functional data analysis. I think you have a good chance of getting into there.

If you go to a PhD program in the US, you may have to 'retake' some of the graduate courses that you have taken since they may cover different material so this will not save you time. If you go to UBC/McGill for a master's, you can waive the courses that you have taken and this will shorten your completion time. Even if you are admitted to PhD program at Toronto, you will still have to take graduate level probability/statistical inference and I don't think you can graduate faster compared to doing a master's at UBC/McGill first. In Canadian schools, if you get into a master's, it is almost guaranteed that you get into their PhD program so I would apply to UBC/McGill. If money is not a concern for you, I would apply to at least 10 schools.

Schools like Stanford, Berkeley and Columbia are extremely unlikely (less than 0.1% of chance) given your profile so I wouldn't bother applying to them. CMU, Washington and Yale are reaches for you. As a Canadian citizen, you have a high chance of getting into Toronto so it does not make much sense to apply to schools below that. I would add other first-tier schools in Canada such as UBC and McGill. With that said, I wouldn't apply to UCLA unless you are really interested in some faculty's research there.

You could take real analysis courses as a non-degree student in your undergraduate institution. Doing well in real analysis will improve your chances at top schools. Columbia/Cornell/Yale are competitive because of their general reputation and small cohort. However, their academic placements are not as good as top public schools like Washington/Berkeley/Michigan.

Your grades look fine if you apply for statistics masters. Wisconsin may be tough to get in as their master's and phd applications are reviewed together. Master's admissions are not super competitive in general and I can see you getting into a few programs you listed.

In this case I would definitely apply to Chicago and Columbia. Although they are tough to get in, I think your chances are above average.

The overall GPA usually serves as a cutoff and you can definitely pass the cutoff so I wouldn't worry too much about it. Since you have strong background in math did well in all upper division courses, I think your profile will be viewed more favourably than someone with 3.9 GPA and low grades in real analysis. I would apply to 10-20 schools since admissions are much more competitive than before. I agree that Chicago/Columbia might be reaches but I think you have a good chance of getting into UNC/Wisconsin/Penn State.

You have very strong mathematical background. A good subject test score will definitely help at top places like Washington/Columbia/Chicago and I think a 80% or even 90% is attainable with some preparation given your background. I think you have a good chance of getting into top 20 and you don't need to go lower than UCLA/Rice.

You have very strong grades coming from a school that is known for grade deflation. I think you have enough math courses but some additional courses such as measure theory/functional analysis may strengthen your profile, considering that many international applicants have very rigorous training in mathematics. Your list looks good and I can see you getting into a few of them. I would apply to 10+ schools with some safer options at the level of Penn State/UC Davis/Minnesota since admissions are competitive for international students. I have a friend from your school with similar background as you ended up into one of the above schools. I would also apply to your undergrad institution. If you are interested in Bayesian statistics and non-parametrics, UBC also has several people working in this field.

Given your current profile, it would be unrealistic to apply to any ranked PhD program. You would need a lot more math courses to be considered. The minimum requirement for admission is calculus 1-3, linear algebra 1-2 and introductory probability/mathematical statistics. However, most applicants have real analysis and other proof-based courses, especially at programs you listed. After completing these courses with strong grades, you may stand a chance at these schools. As for the math GRE subject test, I doubt that you can get a good score with your current background. The test covers all topics at the undergraduate level and in addition to the above math courses, you should also have basic knowledge in ordinary differential equations, number theory, abstract algebra and complex analysis.The test takers are mostly students who intend to apply for math PhD so you are competing against them, and most of whom have taken more math courses beyond the courses I listed. With that said, an >80% is not attainable if you don't have extensive math background.

I am pretty sure you can get into master's program at Toronto/UBC/McGill. Top programs like Harvard/Stanford/Berkeley are competitive for everyone. You didn't post your grades in real analysis/complex analysis/mathematical statistics ...but if you have strong grades in them, you should be at least in discussion at some of them. You have enough math background but I think courses in measure theory will further strengthen your application, especially if you get an A in it.

A 160 in GRE Q could lead to an automatic rejection. For most statistics programs, the average GRE Q of admitted students is over the 90th percentile. So realistically you should aim for 168+ and at the very least, a 165. Higher ranked schools typically require more math, so if you take two semester of real analysis, measure theory and some other proof-based courses with mostly A's in them, you stand a chance of getting into top 20's.

No. As long as you have strong record in math courses, those programs won't care much about your math GRE score.

GRE Math subject test isn't super important except for maybe Stanford. If you can get >80% with 1-2 months preparation, I think maybe it worths taking the test. The test has a broad coverage so make sure you review all the topics. Since you haven't taken abstract algebra and complex analysis so it may take you some time to pick up the basics of these material.

Both of them won't matter much so take what interests you.

Internships do not matter much unless you produce high-quality papers, which is rare for undergraduate students. Your ability to do mathematical proof is the most important so I would take proof-based courses in mathematics or statistics.

How does Indian GPA translate into US/Canadian ones? If your 74% is equivalent to an A- or above and you do well in real analysis/measure theory, you may have a shot at schools in the 30-50 range such as Florida State/UConn/Ohio State and tie-2 schools in Canada such as Simon Fraser/Western Ontario. From my experience, the subject test is pretty useless unless you aim for Stanford/Chicago/Wharton so I wouldn't take it.

If you retake these prerequisite courses and get good grades in them, I think you have a chance at mid-tier master's programs. The general GRE test is mostly used as a filter so you should be fine as long as your score in the Quantitative section is above the 80th percentile. Beyond calculus and linear algebra, the subject test also covers basic real analysis, complex analysis and abstract algebra and I doubt MS programs care about the test. Without a strong pure math background it is impossible to do well so I wouldn't take the subject test.

Master's admissions are much less competitive than PhD's since you pay for the degree. With your profile, if you can get your GRE Q to 166+, I think you should be competitive for the top 10s. I would definitely apply to top schools like Harvard, Berkeley, Chicago and Stanford as well as add some safer options in the top 20s.

If you haven't taken any proof-based courses, I don't think it's a good idea to take grad-level probability courses. I would start from basic real analysis courses. Ideally you need two courses in real analysis covering material such as metric space/norm, completeness of metric space, hölder's inequality/Minkowski inequality(this can be further extended to other spaces such as Lp space and probability space) , basic topology, continuity/uniform continuity in metric space and Riemann integration. It would be better if you had exposure to Lebesgue integration before taking grad-level probability courses since probability space is a special general measure space and understanding Lebesgue measure definitely helps.

Since you are from a top school that is known for grade deflation, your grades should make the cutoff for the schools you listed. In order to have a better chance, I would take real analysis this fall since it is going to be helpful even if you do applied research. If you scored an A- or above, I think this would be a positive sign for admissions committee. I would apply straightly to PhD programs and add a few MS programs.

I wouldn't recommend you take a gap year because nobody knows what the situation will be like in 2022. Since you haven't taken abstract algebra and complex analysis, it would be very time-consuming to prepare for the test. Unless you are dead-set on getting into Stanford, I wouldn't recommend taking the math GRE. You have excellent math grades from a good school, so you should be competitive at the top 15 programs in US News if you can secure strong letters. I think some schools accept fall grades and you could submit them if you do well, which I think will help your case. As for program selection, aside from the top 15 schools, You could also add a few larger and lower ranked programs such as Penn State, Purdue and UIUC just to be on the safe side. Given the current political climate in the US, international student visas are harder to come by so I would also consider applying to a few top Canadian programs such as Toronto/UBC/Waterloo/McGill.