Why Is There a Timer on Tactics Trainer?

And what is the time limit?  

The more time that goes by, then the worse your score.  Personally, I don't need the added time pressure and enjoy chesstempo.com more.

I agree!

bobby -- have you tried chesstempo?  You'll be amazed at how many ending that you are able to solve without the time pressure.

I use chesstempo as well; from 20 - 100 problems a day. Of coarse I'm only at 1430 on there.

Can you get a negative score even after correctly solving the problem at Chess.com due to taking too long? 

Secondly, have you all noticed that sometimes there are more than one correct answers?  At least in non-checkmate scenarios, I sometimes feel there can be more than one answer (or so I think - lol ).

Yes, you start to lose tactics rating if you take too long on a puzzle, even if you get the answer correct.

There is an option in account settings to disable the timer. It also sets them to unrated however.