I am in between 9th and 10th grade ( it is summer now).
This is my plan now:
1.See if my school has a NJROTC program and join it if it does.
Okay...could be a god idea, and could give you a leg up on getting an NROTC scholarship out of high school. Just completed your freshman year, so why don't you already know if your school has a NJROTC program?
2.Go to college under a ROTC scholarship for engineering
NROTC scholarships are hard to come by right out of high school. I can tell you from experience though that if you go to school without a NROTC scholarship, but join the NROTC program, and do well in your first year of school as an engineering major, you'll likely to get a scholarship offer.
3.Go into the navy for nuclear reactor engineering
Becoming a nuclear reactor engineer is not an easy endeavour, especially from NROTC. You want to work at Naval Reactors Headquarters (NRHQ) in DC. There are 22 different sections at NRHQ, and only a couple of them actually do reactor design work. However, every section does important work in support of our navy. You'll need greater then 3.9 college GPA to be competitive to get an interview for any position at NRHQ.
4.Either stay in the navy or leave after paying off my dues depending on benefits and what not
Do this seem like a decent basic plan?
Seems like a decent plan for a rising high school sophomore. Its good to have an ideaq. I know I had no idea what I wanted to do with myself when I was your age!
Now that I'm staring at navy retirement, I still don't know what I want to do when I grow up

And I a question. My dad is an ex-nuke tech and I was discussing this with him and he said that most of the nuke engineers in the navy don't actually engineer any reactors, they just have that done by General Electric and other companies, and that the majority of them just watch over the tech and electricians, is this true?
As i said, there are some chance to do the work you mention in the navy. However, there are other organizations that support the navy and its nuclear power program that also do reactor engineering, reactor design, etc. These companies are Knolls atomic Power Laboratory (KAPL), BETTIS atomic power laboratory, Electric Boat Corporation, and Northrup Grumman just to name a few. They hire good people also.