They fly a different flag, because they are a different country, now if they were the same country, they would fly the the US flag.
Yes, it is legal in the US to fly a US, or other flag, from your car. Many people do that.
Texas
Technically, they are on their own soil, so no, they don't have to fly our flag. Just as our embassies don't fly their flag.
Any state flag should be flown below or level with the US Flag, but never above it. If it is on the same level it should be on the right, this includes Texas. The rumor that Texas is the only state that is allowed to fly at level with the US Flag is just that a rumor and an urban myth.
It could, but it would be disrespectful.
It is legal to display any flag in the US. This is a matter of freedom of symbolic speech.
No
Any flag could, but it would be disrespectful.
In the United States, no. It is improper to fly another flag above the US flag in the United States. Other countries have similar customs and rules.
All official US flags are lowered at dusk, or are never raised to full staff (Arlington National Cemetery, USS Arizona).This question is sometimes a riddle with the answers of "the Alamo" where the flag is nailed up, or on the Moon, where the US flag will fly from its special staff until it falls apart.
It is legal to fly the US flag on a pole in your yard, unless you are somehow doing so in a manner that is disrespectful of it.