Whoa, a lot of questions. I'll divide them:
1. How does the healing mechanism work?
I'm not quite sure, but things tend to heal from broken skin and such over time, leaving a scar. Broken bones may or may not heal, I don't know, as I haven't had many injuries this version. There's nothing you can do to speed it up; even if it was tamed, animal caretakers are bugged completely broken. I'm not sure they ever worked.
2. Should I worry about infection?
Don't. Even if it does occur in non-dwarves, there's nothing you can do about it. Infections aren't a sure-death thing these versions, anyway.
3. Should I pit some prisoners from the Tower of Judgement to feed the beast?
Hehehe... Do keep in mind the prisoners may further injure the beast; stripping them of equipment (by using (d)esignate, (b)ulk, (d)ump on their cages, then unmarking the cage itself) will probably be safer. Otherwise, up to you. Hehehe...
4. Does that [make the hydra] "heal faster"?
No.
5. Do hydras die of starvation?
Nothing that is not part of your group (i.e., dwarves, livestock) will never starve, go to sleep, drink, etc. This means invaders, wild beasts, traders, and diplomats don't need to worry about those things. Lucky...
Also, what's the "Toroid Cyclotron Cannon"?