Going to do my best to answer your questions, let me know if I miss something.
1. After OIS, even though you go to a "Big 3," your tour will be 3 years, not 1 like you thought. All tours in the Navy are for 3 years with a few exceptions.
2. Nurses on ships. As a duty station, yes you have to volunteer for that. We only have 12 ships in the Navy that accomadate/ use a nurse and they are carriers. You have to request to go on one. However, in a deployment situation you could find yourself on a ship, just depends. As a duty station though, volunteer.
vs. uniforms. It all depends on where you work. Most critical car areas are scrubs including most ERs. All the other floors generally wear informs, but places like L&D where scrubs too. This is an issue that is different at each command. If you have a particular interest in an area, try to get some experience there. I always advise people coming in as a nurse to get a job as nursing assistant in the area they like. I liked ER/ ICU and worked for 3+ years in those areas before my license. When I got to my duty station and they asked if I had experience outside nursing school and I said "yes." I got exactly what I wanted, I marketed myself, keep it in mind with 4 kids that's a stretch with school.
4. Family ahead. Yes, once you get your orders they can go ahead. However, you need to provide your husband a power of attorney to get the household goods and stuff like that. If you wanted to do base housing, they can't do that without you. It all depends on what you want them to do without you. Also keep in mind that you won't get paid for the new duty station BAH until you get there, I think, need to check on that one.
5. NCP Time frame. O.K. there is a process for this, it's not sign on the dotted line and you're good, you have to apply. I applied in a year when there 3500 other applicants, they chose 35 that year. Things are probably different now, but you if this is what you want to do, you need to get in touch with a nursing recruiter and get the ball rolling. Once the application, physical, etc., are complete you have to wait for the next board to meet and that can take months. Once you get accepted then you can start getting your money. So what you need to do is get a nursing recruiter to let you know what is going on, where are you located, maybe I can help. I know the guy in Baltimore, MD.
Keep the questions coming and let me know if I can help.