Up to the point of protected speech, yes.

Free speech doesn’t mean you can say anything, anywhere, anywhen. It means that you can expect to be free from persecution or prosecution based on expressing a range of beliefs via speech/press.

There should be a difference between a truly private property, as in one’s home, and a business property, but that’s a different issue. Even with businesses being “private” property, they still have to toe the line with protected speech, and most of the examples you gave would fall under that. The problem comes in litigating the violation