The
Deep Dwarf page on the wiki has a list of ways they can heal. For DDNe's, the big one in the early game will be Vampiric Draining... memorize that spell the instant you hit level 3.
The thing about Vampiric Draining, though, is that it can't cause damage if you don't have HP missing for it to replace. If you cast it when you're fully healed, you won't get anywhere. So only cast it when you're wounded. And yes, it will get more badass with practice (and as your Necromancy skill rises).
EDIT: Yes, if you quit, die, or go upstairs from level 1, you have to make a brand new character. This resets everything, mana bar and all. The only thing past games affect is that if you die below D:2, you spawn a player ghost that future characters might have to deal with on that particular level. That can be both good and bad. (Player ghosts are tough and they won't drop their past gear, but they're also worth a lot of XP.)