When i turn the key on it sounds like the car is already started

Is this chevy vehicle?? Some starters need shims when installed to prevent this type of noise when starting vehicle. If your starter had shims, put it back on nee starter..

Could damaged flywheel teeth where starter mesh. Turn the motor by hand a half turn and then try starter again. Does the vehicle start when you push or tow it?

CHECK ALL WIRING CONN SOUNDS LIKE THE BENDIX DRIVE IS STUCK FOWARD CHANGE OR REBUILD STATER.

does the engine turn over? or is there a clicknig sound or no sound when you turn the key

Sounds like the bendix or selenoid for the starter has worn out.BUT,for the starter to run after you turn off the key,that's just spooky.I'd bring it to a good mech.

Sounds like either the STARTER DRIVE GEAR or the FLYWHEEL
where the starter drive gear engages. With the key off find a belt and try and turn the engine a bit by hand. That will move the FLYWHEEL to a new place. Try starting the car. If it starts then you have a bad wore spot on the FLYWHEEL. If after turning the engine by hand you get the same no start situation in will be in the starter drive itself.

Only if the engine is running,will the loose belt cause a noise in the engine,if it is a grinding noise,the starter drive,may be sliding into the flywheel.

You may have a damaged flywheel but not sure.

IS THERE ANY VOLTAGE TO PUMP? IF THERE IS VOLTAGE LOOKS LIKE YOU ALREADY PERFORMED THE DIAGNOSTIC

sorry to tell you this with all the repairs yopuve already done but im 99% sure you need a new starter.