Can You Shoot Yourself in Bang?
You can get yourself shot by playing a Duel and then not responding if the person you dueling with discards a BANG! Besides that and Dynamite, I don't know of other ways to hurt yourself with your own cards.

However, there are other ways to solve your problems:

(1) Problem of Player Elimination: Add the unofficial BANG! expansion, Death Mesa, to the game. In this expansion, dead players continue on as ghosts, draw from a specialized deck, and influence who wins (all ghosts, regardless of role, can still achieve victory). Visit http://bangcardgame.blogspot.com/p/death-mesa-expansion.html

(2) Problem of BANG! Dragging On: Give BANG! an internal clock through adding one of the following house rules:
-  Play only with 3 life point characters. If you have Dodge City, this gives you 7 characters; The Bullet, 8 characters; with Wild West Show, 9. Or make all 4 life point characters have 3 life points and only play with them.
- Players can shoot as many players as they want per turn (given distance constraints), but they can only fire 1 BANG! at each player per turn.
- If things are really getting slow, you can impose a new rule after a certain amount of rounds: Beer and/or Missed! are not reshuffled into the deck. They are placed in a separate discard pile and cannot be reused.

If you are interested in different house rules, visit http://bangcardgame.blogspot.com/p/fistful-of-bang-variants.html