Nope, none of those things you mentioned would prevent a car dealership from hiring you.

The dealership I worked at over the summer had a few women sales people. They did fine by themselves. One of em was even a complete dunce and didn't know jack about the cars but still managed to sell a decent number of cars.

Aside from the long hours it's an easy job and pays more than decent if you're good at it. Plus you don't really need any sort of qualifications whatsoever. Getting hired at a car dealership is of equivalent difficulty to flippin burgers.