To answer your questions:
1. Typical exercise equipment on a Submarine, T-Hull (SSBN, SSGN) or Fastboat (SSN) Treadmill, Elliptical, rowing machine, stationary bike, dumb bells (maybe, technically not allowed, but sometimes they make exceptions), bowflex or other "rubber band" type. That's about all I've seen of typical exercise equipment. there is a lot of homemade type stuff also (chin up bars, some free weights, those forearm wheel/rope things). One thing there is not a lot of is room. No room for Kata's, sparring, etc (maybe some tai-chi type stuff). might be able to get creative on a BN/GN, but not too much.
2. Volunteering: per the previous poster for school, I guess. But during my time in school there was almost no time for anything BUT school. 8 hours a day M-F, and then 25-50 extra hours after school, most of which is made up on weekends. After school/prototype, when you get to your boat you have got at least a year of "Your DINQ (Delinquent IN Qualification), get qualified NUB (Non Useable Body)". After that, more power to ya buddy. According to Wikipedia (
http://en.wikipedia.org/wiki/Military_Outstanding_Volunteer_Service_Medal) it takes about three years to get the medal. So figure 2 months for boot, 6 months for NNPS, 6 months for NPTU, plus waiting/hold time, 1 year on boat, your looking at almost 1/2 way through your enlistment before you can start. Take the next three years to work on the medal stuff (between deployments / patrols, trainers, schools, other upkeep / refits) and then you are looking at being almost to the end of your enlistment.
It may seem like I'm saying you cannot do it, I'm not. What I am doing is being honest. Typically you spend so much time at work, that there is barely enough time left over for a social life let alone volunteer work. Although now that there are going to be women on subs, you may be able to combine work and social life (just kidding

).
Hope this helps, thanks for your (coming) service, good luck.