Do wizards not have lawyers?

I have been re-reading the Harry Potter series, and I must say, so far it has been quite enjoyable indeed.  However, I've noticed a lot of holes that I've never noticed before.  One of them was, where did Voldemort's wand go after he was "killed" in Godric's Hollow?  Apparently J.K. Rowling has said that Peter Pettigrew went back and got it, and I guess that's fine.  

But this one from Book 4 I'm having a lot of trouble with:  Harry must compete in the Triwizard Tournament because after his name was submitted and accepted, there was a "binding magical contract."  I think that this contract is void (not merely voidable) for at least three reasons:

1. Forgery:  Harry did not put his own name into the Goblet.
2. Fraud:  The fake Moody admits that he put Harry's name in under another school, which presumably would not exist (or at least would not compete in the Triwizard Tournament).
3. Incapacity:  Harry is not only under the age limitation imposed on the contest, but the age limitation is also the age of majority for wizards:  17.  As Harry is only 14, he cannot sign any contract on his own but must have a parent or guardian sign on his behalf (and wizards do recognize this rule, see Harry's permission slip in Book 3).

Do wizards not have lawyers or courts?  Sheesh.