Let me tell you, as someone who has climbed the pyramids at Chichen Itza, I would not do it again. You get to the top and there is nothing up there, though it looks like you might see something cool from the bottom.
But the thing is, it is a LONG climb at something like a 50-degreee angle and the stairs are only about 4 inches deep. I doubt the US would allow people to scale them. One slip and you could easily tumble 50 yards to the bottom.
I went down using my feet AND hands, and I couldn't wait to get to the bottom.
Sorry, I do not know the answers to your other questions! I will say Chichen Itza is worth seeing even f you can't climb the pyramid. There are many buildings there.