A Supreme Court ruling a few years ago guaranteed everyone residing in the U.S. regardless of his or her nationality or citizenship status, all Constitutional rights—the same as U.S. citizens have—before the law. Right then and there a dagger thrust into the heart of America. Right there. Is where it all starts and ends. Where do we get these incredibly enlightened and superior intellects, esteemed and elevated to such high positions of power and authority? Just where?
The basic problem is how you are looking at the rights enumerated (not "granted" or "given") by the first ten Amendments to the U.S. Constitution. You have a natural right to speak. This is given to you by God, not some dusty piece of paper. Same goes to the natural Right of self defense. It is granted to you by God and cannot be legitimately invalidated by the laws of man. This means that a visitor to this country would have the right to purchase and use a weapon. The fact that a specific person is not legally in the country is remedied by removing said person from this country. (I'd like to see the use of catapults us for this removal.)
The other problem, is that you cannot have a welfare state with open borders, or the nation will be destroyed by those who take everything, and contribute nothing. Thomas Sowell spoke about this years ago.