Is there a regulatory board for HOA management firms?

HOA management firms: I think you're talking about property managers. If so they're regulated by the state agency that governs real estate.

I am guessing you aren't talking about property management, but the HOA itself And in that case no, but state law rules what they can and can't do. Essentially an HOA is a local government that exists within the Covenants. Conditions & Restrictions of the HOA. Also known as the CC&R's. Its sort of the HOA's constitution that each home owner agreed to follow when they became titled to a property within the HOA, and you should have obtained a copy when you did. If you think the HOA is acting improperly, the CC&R's is where you will find their error if they are making an error at all. Of course the other option to address issues is to participation by getting elected to the board. Good Luck.

Not as far as I know. HOA like landlords are governed by the court. If they violate the law your primary remedy is to sue them. There are legally required steps in most states you have to follow before you can sue but that also depends on what the issue is.