Try not only having the heat off, but turning the temp all the way down. It opens it up to the engine heat when the temp gauge is set on hot. So you will have a bit of ardient heat floating out.

In my car, I find if the inside has water, its going to fog up pretty crazy. Try to dry things out as well as you can. PPark it in the sun and open the rear hatch, or whatever works for you.

not unless the temperature is set to warm. if it's set to cold you should get a bit of cool air flow while driving. ditto if it's set to warm.