So are you stationed out at sea for ~6 months and at port/homeport/shipyard for ~18 months?
You're stationed on a sub/ship for 48 months. You go where it goes. If it's at sea, so are you (except if on leave/assigned to a school). If it's in-port, you are in a 3-section duty rotation where you stay on board every 3rd night, and are most likely standing port and starboard watches (12 hours on watch) during those days.
What's the real difference between the sub and carrier life? Some reason to and not to go onto each one?
This is too much to answer in this thread. The punch line: fewer people means you'll have more responsibility, so you'll learn a lot more. It also means you'll work a lot more and have less free time. There's also the enclosed, small environment. On a carrier there are a lot more services and spaces, whereas on a sub everything is crammed and multi-purpose.
What are the chances I will get stationed on a fast attack sub instead of a boomer if I request it? I volunteered for sub duty, but I would much rather be on a fast attack sub.
42%. Honestly, as a nuke, it won't really matter if you're on a fast attack or boomer. It's the same job.
I'm near 6'4, will I have a problem with my height being in the subs?
Yes. You won't fit into a rack with legs extended and will have to walk around hunched over in most spaces.
What will I be doing when I'm at shore? From my understand it's a few classroom hours and maybe a couple watches but that's really it.
No. You stand 3-section duty and on non-duty days will be doing a hefty maintenance load. You can expect to be on the boat at least 80 hours a week.
This is my the question I want answered most:
Is there anyway I can finish my 6 month deployment at sea or however long it is, and request to go on a different ship to go right back out? If so how would I go about that? Also if anyone has done that what's your opinion on it?
Go "right back out?" No. If you want to ride another boat while you are in the shipyard, there is a possibility of that. However, it will depend on the needs of your ship and the needs of another ship. If you are fully qualified, the answer will probably be no, since you'll have to suppor the in-port watchbill and maintenance.