Nope. He lives on someone else’s property under their rules. If they don’t let other people fly flags, hang them from balconies, etc., the same applies to him.
I think it is wrong and don’t care what ‘practicing Moslems’ think but private property is private property.
Nope. The flag is speech, protected as primary by First Amendment. Private property does not negate the Constitution.
I think an apartment complex would fall under the Freedom to fly the American Flag act:
https://www.gpo.gov/fdsys/pkg/BILLS-109hr42enr/pdf/BILLS-109hr42enr.pdf
The federal government owns a lot of land in the west United States, roughly 50%. Are you saying that when I’m on federal land I can’t say my mind either?
Also even though he is on private land he is a paying, not a guest. Renters have some property rights of their own. And just because you rent someone’s property doesn’t mean you have surrendered your 1st Amendment rights.