What are the US regulations governing experimental aircraft?
Your first question 


  There are more experimental class aircraft in the USA than any other. That being said, what type of requirements does an experimental aircraft have to meet. 


is very broad and should probably be its own question.

As to your second question 


  Also, are there ways around certain regulations? 


The short answer is "Yes".  You can apply to the FAA for a waiver of specific regulations.  It's commonly done for aerobatic contests to permit aerobatics below 1500', within 4 nm of an airway, etc.  The waiver is of extremely limited duration and calls out the regulations to be waived.  Air shows also have them.

I haven't personally requested such a waiver but I've seen them.

The FAA probably permitted the overflight because the pilot was able to show it was safe, would do no harm, and wouldn't cause them any problems.