The radiator cooling fan is most likely not working.
Yes, it could.
no
It will not cause the engine to overheat. You have another problem.
sometime the fan do not work which can cause the car to overheat. Also it can be a fuse for the fan. Check your thermostat.
yes
No.
No.
YesYes
no it can not.
No
A leaking heater core will cause the engine to overheat because the coolant is leaking out.
If oil pressure is low it certainly can cause the car to overheat. This is because the mechanisms are not being properly lubricated with enough oil.