I'll try and give you some insight.
1.) Why don’t subs become super cold being in deep water for extended periods of time?
There is a ton of electronic gear inside of a sealed tube. It gets as hot as hell without air conditioning. Once we were at sea on patrol and lost a heat exchanger. To do repairs they had to take the entire system off line. It was 112 degrees in the control room forward. The engine room was well over that. They relieved the watch every two hours. Uniform of the day was underwear and tennis shoes. And this is with turning off all non essential equipment.
2.) I know this is movies not real life but they are always portrayed as being really warm. Does the engine/reactor/batteries put out that much heat?
Yes, even the lights.
3.) How often were you able to shower or clean yourself underwater? How was hygiene enforced?
Yes, a short shower every day or so as long as the freshwater evaporators and stills are working properly. I have seen when one goes down and we went for a week or so with no shower water. The reactor always gets first dibs on the water, then the galley, then the crew...
Standard Submarine Shower:
Turn on the water, get wet.
Turn off the water, soap up.
Turn on the water, rinse off.
Turn off the water. ~ 3 minutes tops.
4.) I imagine if one dude smells like ass it is bad for moral or does everyone smell like ass and nobody notices until you get fresh air?
On a Submarine everybody smells like ass anyway from the oil, amine, hydraulics and enclosed environment for months at a time.
5.) Any weird noises happen like something contracting that puts you on edge? Is it a regular occurrence?
The decks are not attached to the hull, but slide as they float on beams. When you go down the hull contracts and when you go up it expands. Short answer it creaks whenever you change depths. You get used to it and usually pay no attention.
The only hairy dives are the first out of the shipyards or the test depth emergency blows.
Take it into account that I retired in 1993. I'm sure things have improved a lot since I rode the boats. They are much fancier now. I worked on some of the Trident Hull boats before I retired and they were like a Lincoln in comparison to an old 608 class boat that I cut my teeth on.