Well you can't just look at the 1st Amendment at face value, you have to look at how courts have interpreted the meaning of the 1st Amendment. And I think you'll be hard up to find a case where something produced as parody was found not to be protected speech. Trademarked names can be used under "Fair Use" for 4 purposes, including parody, news reporting, comparative shopping and something else I cant rememer.
As far as the 1st amendment goes, live by the basic rule of "The first amendment doesn't give you the right to yell Fire! in a crowded theater."
It's true that there is "fair use" of trademarks. However, that is usually decided in court, meaning that you can't assume that you won't be sued simply because you used the trademark in a parody. Also in the case of a parody site, there are issues of potential defamation and libel. Even if the web site is in the legal right, that wouldn't necessarily stop someone from suing you and letting the judge decide - in fact there have been many cases where that has happened. If you are sued, you will need to spend $$$ and time to defend yourslef. The original poster asked "could I be sued", and the answer is "yes".
I don't think there are issues of defamation and libel, because no reasonable person could be expected to believe that something created in parody was a serious claim and therefore claims of defamation and libel would hold no merit. But I agree with you, the OP did ask if he could be sued and the answer is yes. But you could be sued for absolutely anything. People shouldn't be afraid to exercise their rights to free speech just because someone with money might try to stop them. If we allow that to happen, than we deserve to lose those rights.
Absolutely, and, in much the same way that Jerry Falwell was unsuccessful in his attempt to collect damages from Larry Flynt regarding some vicious parody Flynt published in his adult magazine about the evangelical pastor. On February 24, 1988 Flynt was found not guilty for intentional infliction of emotional distress as the US Supreme Court made the clarification that public figures cannot recover damages for "intentional infliction of emotional distress" based on parodies. This however may not be true thoughout the rest of the world. When the Fake News is presented on Comedy Central by the likes of John Stewart and Steven Colbert it is pretty difficult to make the case that it represents complete factual correctness. I would suggest that any parodies you choose to do are not too confusing as to make it possible to argue that some might consider them factual. Of course this would not, in any way make it impossible for someone to bring a case against you, it would however make it difficult to win in a US court. I hope this helps! Best wishes, Kimmy