Signs of a transmission failure are poor shift quality. It may take too long to shift or the RPM's will go up and the car will not increase in speed. You may experience noise coming from the transmission either a whine or clunk noise. The transmission may have slow engagement or not want to move at all in drive or reverse. The transmission fluid condition can be checked by looking at the fluid on the dip stick. If it is brown or black it needs replaced. If it smells burnt the transmission has been slipping. Some cars do not have a dipstick. If this is the case you will need to have it checked by a shop. The check engine or service engine light will come on for transmission problems. On Fords the OD light will flash. As for leaks look for spots on the garage floor or put card board under the engine and transmission and check for spots in the morning.
The clutch and related components are part of a standard shift transmission. The clutch system is designed to disengage the engine torque so the manual transmission can change gears. The clutch disc has a friction material on it that is designed to wear. The disc is located between the flywheel and the pressure plate. When the clutch pedal is pushed down the spring loaded fingers on the pressure plate pull the pressure plate away from the clutch disc disengaging the engine torque. Releasing the clutch pedal engages the torque of the engine by putting pressure on the disc against the flywheel. The flywheel is attached to the engine. Warning signs of a clutch failure are vibration when releasing the clutch pedal in first gear. A clutch pedal that doesn't engage until the pedal is near the end of it stroke. Grinding noise when changing gears or difficulty shifting gears.
The flex plate attaches to the engine crank shaft and serves two purposes. It has gear teeth around the outer edge and when the starter is engaged the gear on the starter interlocks the gear wheel or flex plat. This action cranks the engine allowing it to start. The flex plate is also connected to the automatic transmission torque converter.