I recently bought a 2003 model 2.4 cherokee sport model with a few issues. Please help!

Firstly, the oil light sometimes stays on when you've started the vehicle. Only happens every once in a while. Switching the car off and back on can make the light go off. I've read somewhere else that it can be the oil sensor??

Secondly, the interior lights and electronics seem to all work, but they seem to be out of sync. When i switch the headlights on, the speedometor and radio lights go off. When i open the door, the mileage indicator comes on etc. It seems you cant switch off the headlights without turning the stick twice. I.e you have to switch them off, switch them on then switch it off again.

Lastly, whilst driving the vehilce seems to die and then spring back to life seconds later. This has happened twice while i was driving on the highway. Its almost like you've turned the key back to switch off and then seconds later switch back on.