Can mot inspector test his own car?

Go off road and test it their. Put power to it and see if it works. There is only one wire on it and that's the power.

Not unless your name is on the title. Possession of the title does not mean you own the vehicle.

You may have to add their name to the title as co-owner.

It depends on what you mean by "Primary" owner. If you mean that two people signed together to buy a car, if one dies, the other takes possession, period. If it has no liens, cosignors, etc., on it,...

yes