is i signature on a paper a legal document?

You agreed to settle your claim against the hotel in exchange for a refund of the amount you paid for your stay.  The question is whether that agreement is enforceable.  Normally, even where a contract is required to be in writing (most contracts are valid and enforceable even if only oral), all that is necessary is the signature of the party against whom the contract is sought to be enforced, or its agent.  Here, you have the signature of the hotel general manager, which would normally be sufficient.  However, some jurisdictions have stricter rules for settlement agreements, requiring, for example, notarization.  I don't know whether Florida has these requirements.  If it does, your contract may be unenforceable, but this could be a good thing, since, if the settlement agreeent is unenforceable, you would still have your claim against the hotel for the bed bug bites you suffered, which I would think is worth more than one free night's lodging. There could theoretically be a quesiton about whether the general manager was authorized to make this agreement on behelf of the hotel, but a person in that position would almost certainly have implied authority and/or apparent authority to do so, even if he/she didn't have actual authority (I won't get into the differences between actual, apparent, and implied authority; suffice it to say that it should be a non-issue.