First thing to consider is that when the clock gets to certain time you are no longer requiere to write down the moves.
So lest say you still have 30 minutes in your clock, and the oponent have 4 minutes. You will be require to write down each single move while your oponent will not be requiere to write down any move. This will eat up all your time before the oponent even spend 10 seconds.
Now if you are 5 minutes and the oponent is 20 seconds, none of you is requiere to write down anything, and indeed you can just play untill all his time is down to zero. Then you win.
About your second question. Yes you can force a 3 moves repetition and make it a draw.
Also if there is 50 moves and not kill of any piece and no pown have move, then it is draw too.
If you see you can force the Draw and want to go for it, it is polite to first offer it to the oponent, maybe he agrees. If he doens't agree then go for it untill the draw happens or the oponent offers it to you... no need to waste time if you can just agree.
This is going to be a retarded question obviously, but I'm curious. Say you're in a tournament and down a lot of pieces, but up on time. Couldn't you just keep on checking the other player and win on time? Or if he can only move his king to two squares, keep putting him in check and draw through three fold repetition? I think Aronian used this to get a draw in a game yesterday.