Illegal immigration has got to be stopped but at the same time we have to keep legal immigration quotas in place. No way could I support open-ended immigration, even if it's legal.
Everything else you say is correct, stop the foreign giveaways and end the welfare.
Agreement at last. Ending the welfare fraud is something else libertarians are big on. A hand up is one thing, but the hand outs have GOT to stop. Absent that, the "legal" immigrants would be less of a problem than you might think.