Have a look at this game:

http://www.chess.com/livechess/game.html?id=1879143

the position being a dead draw, my opponent makes a gazillion idiotic moves, refuses my draw offers and in other ways makes a jerk out of himself.

He tries to win on time in a dead drawn position. DEAD DRAWN.

I got bored with meaningless back and forth, so I resigned.

However, afterwards, realizing what sort of abuse this was, I would like to know if the 50 move rule is implemented in Live Chess.

I am going to play several more important live chess games (in a tournament) here. I'd like to know that this sort of abuse is impossible.

50 moves didn't pass...

I know, I am asking whether that rule was implemented and it was worth waiting.. :)

There is. You make 50 moves with no pawn advancement and no capturing, then click the draw button. Your opponent does not have the option to refuse, the draw is implemented autmotically (claimed, not offered).

Which is precisely how the rule is written.

The difference between legally claiming a draw and offering one isn't clear on live chess

when you click "DRAW", if you are able to claim it (repetition, 50 moves), it will claim. if not, it will draw.

That's because it's up to the player to recognize when the opportunity to claim the draw has presented itself.

I click the DRAW button a LOT.

Wow...there must be a lot of draws in your game archive, DRAWMaster.