Lumping six points into one short paragraph is the problem. Individually, each will need to be addressed... eventually, but not now.
Only the first one needs doing immediately and none of the others needs to be discussed until the first one is a fact and not an empty government promise. Once the border is secure the other points can be addressed but not before.
About half of all illegal immigrants in the USA today are not Mexicans. While a lot of people pass thru Mexico to get here, a significant number fly in on tourist visas and never return.
Good visa enforcement needs to be done as well. We use computers to track every person going onto a flight at every airport. I just flew cross-country this past week; believe me—I was logged to get in the airport and then the plane—surely we can monitor whether or not someone has left or overstayed their visa?