That is correct. Jesus said render unto Caesar that which is Caesar's, Congress shall make no laws respecting the establishment of religion, being a church alone is not reason to get a tax exemption, and clearly the law as it is has massive holes that are being exploited. Their money that actually does go directly to charity should be tax deductible, but that should require them to become non-profits and thus becoming transparent in their finances, requiring them to disclose to the public where that money is going.
If they need to see that they probably aren't very charitable to begin with. And when it comes to politics, it's a great thing if they don't get involved. People's rights get infringed upon and the innocent get harmed. Religion simply has no business in politics.
None that I'm aware of. I've heard of them and people saying they know them, but to my knowledge I have met none.