Is there some common constructions to soften the imperative form and make it more polite like "please"("Ak hem, tack"?) or "kindly" or "would you please"?
you could add an "är du snäll" to the end of the imperative. It softens the blow a bit. (directly translates to "are you nice," but basically means "please")
No, åka is ’go (by vehicle)’. It could also be a bike or a plane. If you want ’drive home’ it would be kör hem.
Literally, yes. In practice, you might say gå hem! colloquially even if you knew people are e.g. driving.