Carbon fiber is just that, a fiber. It's already very strong in tension. Like any fiber, it has little strength in compression, because the fibers are long and thin.
I'm not aware that you could improve it by heat treating it, since it's already been heated. Some, at least, is made by roasting rayon fiber.
Graphite is a form of carbon. You could coat the carbon fiber with graphite, I guess. That would make it slippery, which in a composite, is A Very Bad Thing.
You need to do some reading. First, you need to understand the difference between 'carbon fiber' and 'carbon fiber composite'. You are clearly confusing the two.
I know carbon fiber composite is all the rage these days in real race cars, where it has some virtues that offset its cost. But it's not magic. It's really just a bit stiffer and stronger than glass fiber composite, so it can be made a bit thinner and therefore lighter.
I'm suspicious that a lot of faux carbon fiber composite is also being sold for faux race cars, but that's another discussion.
Now, as for making a submarine hull out of carbon fiber _composite_, yes, it's possible. It may not be the best material for the job. It's certainly not the cheapest.
Before you get too much farther, you need to get a price for a couple miles of carbon fiber tape.
Mike Halloran
Pembroke Pines, FL, USA