1. Typically, you apply by second semester, and are accepted for sophomore year. I'm sure it's possible to apply to transfer after a semester abroad for sophomore year, though.
2. So long as you keep your grades up, maybe. Your high school grades will still comprise the bulk of your application, though, so you may not get into Fordham (I don't know your stats, so I can't comment on NYU).
3. See 1. I don't think you can even transfer for spring semester at most colleges, and trying to do so at this point will mean that you are essentially applying in the first place again, as the colleges will only have your high school record to evaluate. So yes, it is better to wait.
4. No. See 1.
5. No idea! Just keep your grades and ECs up, wherever you are.
Good luck, and have fun abroad!