For #1, it could be the clutch,  and it could be the pilot bearing in the flywheel dragging.
Is the free pedal adjusted correctly? The clutch pedal should move about an inch at the top before you feel it engage the clutch. If you have several inches, the clutch isn't opening up enough. If it isn't the free pedal adjustment, then the clutch will need to come out.

If you don't have a belt pulley drive on the 77, you can remove the bell housing and shaft without pulling the motor. Remember to pull the PTO drive shaft out before trying to remove the bell housing and shaft.


For #2, it sounds like the clutch is slipping, big time. On the 66 you can pull the clutch with the motor in, whether or not you have a belt pulley drive. The PTO drive needs to be removed on this tractor as well.