Alright then.
1. Do I need and college experience? (if so how much)
Enlisted, no. Just a high school diploma.
Officer, yes. You'll need a bachelor's degree.
2. What classes should I take in high-school?
Enlisted, definitely take algebra I. Physics, chemistry, and mechanical principles are nice but not requirements.
Officer, take calculus I and calculus based physics.
3. What is minimum GPA for nuke?
There is no minimum GPA requirement for enlisted. Instead, you take the ASVAB (Armed Services Vocational Aptitude Battery) and possibly the NAPT (Navy Advanced Programs Test). If you score high enough on those tests, you're eligible for the nuclear program (along with various other requirements.)
If you received a D or F in any high school math class, you'll need to get an academic waiver approved.
For officers, you're going to need at least a 3.5 GPA in a college engineering program to be competitive.
4. How long is the navy nuke program?
The initial training is approximately 15-18 months of classroom and hands-on training (plus two months of boot camp), broken up into three major stages. 'A' School, Power School, and Prototype.
5. How long does it take to work off the cost?
Enlisting in the nuclear program requires a six-year commitment. You can, of course, re-enlist after that.
I'm not sure about the officer requirements. GC, would you help with that?