Econometrician

I don't think your profile is atypical really. Yes, I think getting at least one LOR from faculty would help & make you a competitive candidate anywhere

I agree with the above. I think you're definitely the type of atypical applicant that would intrigue most departments, so I imagine you'll have a good shot at most places

Faculty at Columbia do not advise or work with Master's students at all. I don't know about Chicago.

I think if you do well in Real Analysis you'll be competitive for any program (stats and biostats both), so I wouldn't worry about your chances. As for Masters vs PhD, you can always drop out of your PhD and get a Masters after passing quals, so I'd probably also say go for the PhD (since it's also paid plus if you like it you just continue).

I imagine most don't (i) keep their LinkedIn up to date or (ii) don't find it important to add internships to their LinkedIn.

Well, like you say, UChicago is heavy on theoretical, and CMU does a lot of more applied stuff. Personally I'm more into CMU's research and vibe but you seem to be more into UChicago's, plus I honestly think you shouldn't worry about a 'dangerous location' too much, as it's not likely to actually be dangerous unless you wander into the sketchy places. And I do think living in Chicago rather than Pittsburgh is a big step up if you care about social life at all. So, you know, given that you prefer to do theoretical stuff and to go into academia later, I'd probably say UChicago. But CMU is a great department too.

I don't think you're too aggressive. Looks like a solid profile

Honestly, I would be very surprised if you did not get into any of the programs you listed. But if you're looking for more programs to apply to to be on the safe side, literally just go down the ranking list and see which ones you like. I think below the tier you're looking at right now, admissions should be pretty safe for you.

Might be a mistake.. https://www.reddit.com/r/gradadmissions/comments/s6h6so/upitts_admissions_system_is_glitching_got_a/ that really sucks if that's the case

Hi everyone, During my time spent lurking on this forum, I've noticed that the vast majority of statistics applicants that post here are either American or Asian students, with barely any continental European representation. Of course, this is not just a phenomenon on this forum - besides the top French schools, European universities don't seem to send many students to US PhD programs at all. So, that brings me to the purpose of this post -- could individuals involved with US Stats departments shed light on how (students from) European universities are regarded? To make the question more concrete, how are top continental European universities, such as ETH Zürich, the University of Copenhagen, or the University of Amsterdam regarded? Are applicants from these universities at a large disadvantage as compared to those from US or top Asian schools? Any insights on this matter would be very welcome and helpful!

Might be worth trying here, too: https://forum.thegradcafe.com/forum/48-mathematics-and-statistics/