1) Are admissions tougher for FT programs than PT ones, or are they the same?
Generally, admissions for FT programs, especially those in the top tier, are far more stringent than the PT programs. There are several reasons for this. The main reason is that the statistics for PT programs (avg. GMAT, GPA, etc.) are not reported for rankings, just the FT stats, so they can be more lenient since it won't affect their school's ranking. Additionally, the PT programs usually have larger enrollment capability and are revenue generators for the schools (with higher tuition and better marginal profits for the school). This provides a built-in motivation for schools to "compete" for more students in a traditional consumer/retailer model.
2) Are there advantages in applying to a particular round? Is applying in an earlier round better than applying in a latter one?
It is commonly thought that the earlier, the better when it comes to application round. Logically, this makes sense because in large part, filling seats at schools is a game played by the committees. They need every seat filled, so they will try to do so as quickly as possible to avoid the possiblity of leaving empty slots. If they like a candidate, the candidate appears to be qualified, and the candidate will accept an offer and put down a deposit, the "bird in the hand" strategy seems to work for most schools. Plus, they can't always guarantee that holding out for a "more qualified" candidate will yield better results. Some say first or second round is about the same odds, but my experience shows that first round seems to be a better bet if you are ready. Better to put it off and submit a better application than to rush just to get in a round one app.
3) Does my financial aid app have to be submitted once I've sent my school app or can I submit my financial aid app now to get that out of the way to concentrate on my school app? In most cases you are not going to have an open file without an application, unless the schools allow you to open a file electronically first. Once you have an open file, you should be able to submit components as you have them ready, but check with the individual school, as some require you submit everything including financial aid at the same time.