I cleaned the brushes on my starter and got it working but when the gear on the starter came in full contact with the flywheel on the engine it stopped. What would make this happen and how can I fix it?

I forgot to add in that the engine is free to move with out the starter so the engine isn't frozen shut.

the teeth on the starter could be improperly alligned, causing the starter to bind when in contact with the flywheel teeth. Try moving the starter to give it a little clearance.

Also make sure the batterys fully charged, and your connections on the battery are good (no corrosion and are good and tight) a weak or corroded up battery would have enough juice going through the wire to spin the gear up to catch the teeth on the flywheel, but not have enough "go" to spin the engine over, though if the teeth aren't aligning, just go back and fourth turning the starter key till it catches, easier then taking the starter gear cover off.

I was wondering if I could use my car to jump the tractor? Would this be safe and would it work?

As long as the car is a 12volt system (don't have the car started though) its alright, I've done it many times.

i start the car for the extra kick it works well and the motor cranks fast for tuning and rough starting

Did you fix the problem? What was it?

Weak battery or worn bushing in top of starter or wrong starter gear for flywheel, such as plastic gear to steel flywheel, or steel starter gear to aluminum or plastic flywheel gear.
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Yeah I fixed it. The problem was that the battery was dead. I used one of those portable jump things. Now when I get the engine started will the battery be charged from the engine like in cars or will it still be dead?

should charge, let it run for a while.

Yes it should charge...... but if the battery gets weak and dies again, and you have to charge it again ( assuming this is a good battery to begin with ) then it most likely isn't.