It's such a complex issue, but in general the tenets need to be:
-Work with Mexico and Central America to get those who wish to come here, to come here legally (though as I'll tirelessly say again, most come through an airport, and overstay their visa, no stupid wall is going to do that). It worked well when Mexico was actually extraditing people back to Central America that was using Mexico was a through way. Instead of alienating and antagonizing Mexico/central america.
-Those who are here illegally, if they are committing no crimes other than overstaying, get them on a path to citizenship, that will quickly get them to paying taxes rather than dodging them (though the businesses are doing more of that issue). Deporting noncriminals only costs more money, rips people apart, and takes too much time and resources.
-Any of those are committing violent crimes and the like, send em out.
-Wall is a waste of time and money. Just patrol better.
-In terms of limits on how many, IDK, it never really worked properly in the 1800s, can't imagine it working that well today. You can try, but ultimately if they want to come and can prove they can make it work here, I don't see a problem.
The assimilation issue is part an immigration, part totally something else. Other groups that came here created little italies, chinatowns, and the like. It may bother you, but you kind of can't stop it. It's not really illegal to only want to speak Spanish. As long as you are adhering to the law, you just kind of have to deal with it. And assimilation goes both ways, you got to walk you walk towards them too, you can't just dictate them to you.
As for refugees, it's fine to vet them, not sure what "extreme vetting" means to Trump but in general, get them documented, check their background, accept them, disperse among the country, monitor as necessary, and move on. Just don't make it last too long, you're hurting them and not really helping you. The humanitarian benefit makes America look like a partner to the world, which helps our rather tattered image.