The answer to your issues are
1.  Do not provide free education for persons not in the country legally.
2.  Stop allowing currency to be sent or taken out of the country.  I've visited places where this is the case.
3.  All criminals, regardless of status, should be incarcerated.  Using your example, no one would ever be processed judicially or incarcerated, regardless of status.

What I'm saying is that our government does have certain powers to control or abate these issues, should it choose to do so.