1) I am about to enter my first competition next month, so I don't have any suggestion of easily winnable competitions; but, here is the AHA's comp schedule:
They should all have decent judges that are capable of offering some solid feedback.
2) I believe the general rule is you will pay the entry fee per beer, not per category. But, it might be worth checking with whichever competition you decide to enter.
3) This is my first and I only have one, maybe two, that are competition worthy IMHO.
Hope this helps.