Absolutely. The birth certificate issue is only one aspect of the eligibility question. Laws governing citizenship in 1961 determine whether Hussein is a NBC or not and a strict interpretation of them indicates that he is not (father a British subject; mother too young to have attained US residency requirements). A SCOTUS decision is the only thing that will put the NBC matter to rest.
No they don't. The meaning of Natural born citizen, which cannot be changed by law, and the facts of his birth, determine his natural born status. Statute laws cannot change the meaning of Constitutional terms. Otherwise the Constitution isn't worth the parchment it's written on.. oh wait.. well I'm not quite ready to concede that just yet.