@HThorton The transfer admissions process is far different from freshman admissions. Apart from Columbia, I would say you have 0% chance at gaining admission into the schools you mentioned unless you did something truly extraordinary (which is a catch-22: if you really were to say publish in ApJ as a first author you would need to really develop strong relationships and take advantage of all existing resources available a GT and there would not be a reason to transfer), for reasons that are not your fault.
The 4 institutions you mentioned all tend to select most of their transfer students from genuinely non-traditional backgrounds; this is particularly significant because between the 4 of them there are <100 total admitted transfers annually. Quick Google searches of the backgrounds of Princeton transfer students and the CDS of each school can confirm this is the case. Based on your post I am assuming you are a typical high school student and are not a veteran (in Princeton’s case 8 of the 13 admitted students were veterans), someone from a lower quartile of the income bracket, someone who has had significant educational gaps, etc. This is further compounded by the fact that you are matriculating into GT, which in its own right is an excellent school - you are less likely to receive as significant a benefit from attending MIT as someone who from a non-traditional background and are therefore less likely to be viewed favorably for the purposes of admission (though this aspect is less true for Columbia which admits the greatest number of transfer students between the 4 with a 5-6% admissions rate).
If you really are unhappy with Georgia Tech, please take a second look at Berkeley, Cornell, UIUC, UMich, and UCSB, which all reserve spots for typical transfer students.
To directly answer your questions:
1.) Maybe give it one shot each, and this is a huge maybe, but your college performance is significantly more important so only retake if you have so much free time you are genuinely coasting through academics.
2.) Good question: it depends. For the purposes of admissions, applying early will allow you to finish more progress of your degree in the college you intend to transfer to, and in general I suspect most private universities prefer sophomore transfers. However, a huge question you will have to answer when writing your essay is whether you have fully explored the resources at your school and why it is not a good fit with your academic goals - and it is possible that if you are applying in November of your first semester at GT you might not have a compelling answer for this question. Sophomore transfers evaluated both on their high school and university performance, while junior transfers are almost entirely evaluated on their university performance, so which is more beneficial will depend on the person.
3.) Get a 4.0. It’s more than possible to get a 4.0, do research, live healthy, and be socially active; you just have to live like an adult and budget your efforts/time incredibly efficiently.