Uhh... Authoritarian much?
I am going to treat this as "it depend" because it really depends. If you are causing trouble in McDonalds, then he or she has the right to warn you to stop causing trouble or be arrested.
I agree with mathgeek. It depends on the situation. If you're being detrimental to society or someone in particular, or the safety of people around you, then absolutely. If it's just random like "lie down on the floor because it looks funny," then obviously not. If it falls in line with his job, then yes.
It depends, if he says hey stop pointing guns at people,and you keep doing it, he should be able to do so.
Yes, as long as he does not ask you to do anything illegal or morally unjust.
Yeah as long as he doesn't use excessive force.
You run a very fine line with this one; the police force is meant to serve citizens, we are not meant to serve them. If this was the case, police officers could demand almost anything out of us.
Only if he has a justification for asking you to do it. If it is on your property, for instance, he needs a search warrant and can't arrest you for not letting him in.
Depends on what that something is.