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.
Buy ammo, go to the range and get physically fit.