"What can cause slipping of the clutch or its incomplete disengagement when pressing the pedal?"
Clutch slip is manifested in the fact that with a completely serviceable engine, the car does not overcome climbs well, accelerates slowly. This can be caused by oiling of the discs, their strong wear, a decrease in the elasticity of the springs, and the lack of free travel of the clutch pedal.
Incomplete disengagement of the clutch causes difficulty and noise when shifting gears and can lead to premature failure of the synchronizers and accelerated wear of the transmission teeth. This malfunction most often occurs when the discs are dirty, warped or deformed, the position of the release levers is incorrectly adjusted, and also when the clutch pedal is too free to play.
It should be borne in mind that the noise in the gearbox is not always the result of incomplete disengagement of the clutch. This noise can be caused by worn or misaligned bearings, or worn or misaligned bevel gears. A strong knock in the indicated places indicates the presence of a serious malfunction that requires an immediate stop of the car and repair of the unit.
"What can cause difficulty shifting gears or their spontaneous shutdown?"
Difficulty in shifting gears or their spontaneous disengagement is the result of wear on the locks and latches or the gear shift mechanism drive. There is no need for a major overhaul here.
You can prevent such malfunctions in the following ways: periodically carefully check the reliability of fastening of all units and parts of the power transmission, as well as monitor the oil level in the gearbox and change it in a timely manner.