Yes, your NSU ID is that number. It's also been attached to most of your emails that they've sent you (a couple times following "NSU ID:", 😉)
No, if you aren't from Florida don't fill out the residency application. Non-residents stay non-residents for the four years as far as NSU is concerned. It's on their webpage.
You should know if your pre-reqs are met from the letter associated with your acceptance letter, the one listing your provisions. If all it lists are transcripts from your schools then you should be fine. Just send the deposit now but send the other stuff ASAP for peace of mind. I'm sending all of mine as soon as I get my grade back for my last course I'm currently taking. Also, you can check the AACOMAS you sent them in PDF by going to your AACOMAS application online and downloading it. It ought to tell you if you are deficient any credit hours. Obviously NSU doesn't need to follow that to the word but it would be a pretty good indication. Are there any particular classes/credits you are worried about?