The first two appear to be rhetorical questions using the conditional; the meanings are:
1. If he has his own, he wouldn't steal your car.
2. If he had his own, he wouldn't steal your car.
As such, the first breaches the rules of Conditional I and should be emended to:
1a. If he has his own, he won't steal your car.
I agree with your view on 3 and 4. The former is a use of the 'would' conditional as an ameliorator-- a distancer-- for the request. The latter is classic Conditional II.