When the new Mosque is completed can I stand across the street from it with a poster depicting Muhammad stabbing Uncle Sam in the eye?
Yes. The US constitution protects that right. As HB has said, it also protects the right of the local muslims to build it there as that, quite clearly, comes under the umbrella of practicing their religion. If they own that lump of ground then they have a right to build a mosque and practice their religion in it. I don't think that's 'implied', it's obvious. The only area of law that would prevent them from doing so is planning law and that cannot, as per the constitution, be made along religious lines. The question is not: why does the law not prevent it; it's: how could the law, framed within the terms of the constitution, prevent it. But their right to build it does not conflict in any way with your (or any protesters, as you've said you don't have a problem with it) right to protest.

Islamic law, or what I know of it, say that the pictures or a likenesses of the prophet are not allowed
You're not bound by Islamic law so where's the issue. Those who are bound by it choose to be.

Aren't the people, who think it's an unwise move, generalizing the war on terror as the war against Islam?
Unfortunately that can be applied to both sides of the debate. There are muslims who make the same false equation and if the founders of the mosque fall into that category then it would be offensive.

Personally I think the mosque could be a good thing depending on how it's handled. If it's set up peacefully and reaches out to the community it could actually go a long way toward demonstrating that Islam != extremism and building some much needed bridges in the US. If, on the other hand, it is confrontational, it's going to make things far worse. I think the fact that this mosque can be built (protests aside) is actually a wonderful example of how open and tolerent the US really is (despite what us Limeys enjoy implying) and I hope that openness doesn't get thrown back in their faces.