> If marking chalk on a car is trespassing then wouldn't throwing a newspaper in someone's driveway also be trespassing?

Yes, without permission, dumping on someone's property is a trespass.

> So to would leaving a hand print on someone's car if you happened to touch it.

It is a trespass, yes. Probably not on its own an actionable one (or at least not one worth civil action) because of the lack of harm, but whether a trespass would be actionable or worth action as tort is irrelevant in the case where you are looking at a Fourth Amendment violation where any trespass by givernment for gathering information to be used against a person (as a violation of legal property rights) is, ipso facto, a violation of an expectation of privacy, triggering the requirements associated with a search.