the distributor is the likely culprit.
No it would not as it is for emissions only and has nothing to do with engine running. If you have a problem then you will need to have the engine scanned for codes and diagnosed. That should fix your running problem. If you have not replaced the fuel filter in the last 2 years or 30,000 miles then that should help the situation.
Its not your engine. Its the fan running to cool the engine down. They all do it and nothing is wrong with your car.
no as long as the engine is running the pump needss to remain on
oil can be leaking from higher up on engine. u just need to clean engine, then after running for awhile, look for leak, be aware that oil on engine can be blown back over engine by the fan, so some hard looking may be what it takes to find the problem
Not a problem unless you plan on running the engine... Of course it is a problem. An oil filter is mandatory for the life of the engine.
Nothing provided the engine is not started up. With no oil, a running engine would eventually seize up.
No it will not. YOU have another problem.
It is not supposed to be on when engine is running unless there is a problem.
Many times an electronic fuel pump, that is going bad, will cause the engine to stop running and then start again. The fuel pump will eventually get worse.
No, an engine idle RPM being not zero is not a problem. If the idle were zero, the engine would not be running!
The power steering module has lost the engine speed signal. This is normal if the engine is not running. If the fault code comes up with the engine running, you have a problem.
Your statement is a little inconclusive. Will the transmission shift when the engine is turned off, but not shift when the engine is running? If it is jammed and refusing to move even with the engine off, the problem will be inside the gearbox and usually related to the selector forks and or rods. If the the problem is there only when the engine is running the problem will be related to the clutch assembly, which is failing to disengage the gearbox from the engine