If i put a header pipe on my engine with no tune pipe, will the engine still run good?

No, a 2 stroke engine needs back pressure to make abunch of horsepower, this set up is fine for a 4 stroke but all it will do on your 91fx is make it loud, lose horsepower, and wear the motor out. But anyway it is essential that some kind of pipe be on a s stroke to keep exhaust held up alittle. hope this helps

Yes it will if you have a pump to deliver the fuel.It will get more power than with a stock muffler.

Not just a header though. It needs some sort of expansion chamber.