Should NY not allow the Mosque to be built there? Why not?
The city, or state, cannot legally forbid the Islamic Center (not specifically just a mosque) from being built there without showing that it would violate some building code, or other legitimate objection. Just because it happens to be close to ground zero is not a good enough reason. On the other hand, it may be showing incredibly poor judgment by those building the center to choose that particular location, simply because of the negative connotations. Still, this is a free country, supposedly, and freedom of religion is guaranteed in the Constitution. Yes, that same Constitution which the religious right accuses the Obama administration of trying to destroy.

But what about the projects and incidents mentioned in the story above?
Again, the Constitution grants freedom of religion for ALL, not just Christians. Those "demonstrators recently who wore 'Vote for Jesus' T-shirts and carried signs that said: 'No Sharia law for USA!,'" don't seem to realize that trying to establish of ANY religious law is equivalent to trying to establish Sharia law.

Still, exposing the hatred and bigotry of the fundamentalists is always a good thing, as it ultimately reduces their hold on people and exposes them for what they truly are: Christian (in this case) terrorists.

Is that as understandable as the tensions in NY?
I'm not sure any of it is understandable, though the tension in NY is the least surprising.

I was particularly impressed by the following quote:
"If the Wisconsin mosque had not been allowed to be built, I, at 17, might have put up walls and become a different person," [Zuhdi Jasser] said. "If we start preventing these from being built, the backlash will be increased radicalization."

If we want to see terrorist camps set up in the US, isolating and attacking peaceful Muslim neighbors is the right way to go about it. After all, that's basically what got things started in the Middle East, more than a thousand years ago.