>1. Make it illegal to hire undocumented immigrants.

It is, in fact, illegal to hire undocumented immigrants. Federal offense actually. https://www.law.cornell.edu/uscode/text/8/1324a

>2. Foreign specialists need to earn at least an x% above industry standard (to prove they are specialists).

The current standard is that they should earn the pervailing wage, so at minimum average. I agree that they should earn at least 200+% more, however.

I don't think your cruelty argument holds.

>It is, in fact, illegal to hire undocumented immigrants. Federal offense actually.

So then where are all these illegal immigrants getting hired?

"Law on the books" and "Law enforced" are very different.