Is professional photography allowed here?

Yes

Yes and there are very scenic areas to take wonderful pictures.

Definitely

It is, although props may be an issue depending on location and the type of props. I know there was an issue before with a cosplay shoot where someone had a foam gun and park goers began calling the ranger station thinking it was a real firearm. Aside from that, there should be no issues. I see holiday card, graduation and maternity shoots all the time.

Yeah you can

I believe so