1) An RN-BSN program is for people who attended a community college nursing program and got their ADN, took the NCLEX and got their RN. They're associate's degree nurses. In general, it's much harder to find work as an ADN nurse since so many BSN nurses are surfacing and a BSN is obviously preferred over an ADN. If you do manage to get a job as an ADN nurse, you're pay will be significantly lower, hence the RN-BSN program. This way, once they have their associate's degree RN license, they can do the RN-BSN bridge in about a year and get their BSN. I know there are a lot of these bridge programs available online, which is a pro. Also a pro would be the fact that it's typically cheaper and much easier to get into an ADN program vs. a BSN program. However, a con would be that it would take longer to get your BSN RN if you chose this route (about 3-3 1/2 years vs. 2 years, assuming you're a transfer student who has already completed prerequisites). If you're not a transfer student, add an extra 2 years to those times.
2) I don't live in NY, so I can't help with this one. Google BSN programs in New York and you'll get a ton of schools (I assume...) and then look into each one's program description.
3) Sorry, it doesn't look like I'll be much help here either considering I don't know New York or their schools. It's a good idea to have fall-back schools though. I know here in CA, people apply to basically EVERY school in the state that offers a BSN program because the competition is extremely fierce. If you don't have a 3.7+ GPA in the prerequisite courses, you're going to have a tough time getting in.
I would recommend, seeing as how it LOOKS like you're coming straight out of High School, to go to a community college and take care of the prerequisites you need for a nursing program. This will save you THOUSANDS of dollars. Once you have all the prerequisites done (Micro, Anatomy, Physiology, etc.), you can apply to nursing schools and will be able to get your BSN and be eligible to take the NCLEX for your RN.