On Immigration After a Fence

Suppose that a fence is built that is able to greatly stem the tide of people illegally entering the country. By greatly, I mean at least by half and preferably by an order of magnitude (90% or so). Now what?

Well, here's a few points I'd like to see addressed:
1) untangle the path to a visa
Stories like that of jockey Edgar Prado's mother who had applied for a visa in order to obtain cancer treatment in the US, only to finally receive it the day before she died imply that the system is hopelessly inefficient. (Attacking inefficiency in government is to tilt at a windmill. Heigh-ho, Rocinante!) If it were possible to screen faster and still weed out the criminal element, so much the better. If the frustration at having to wait for years for a visa is eliminated, it should also reduce the need to run pell-mell for the border.

2) If we really need a horde of underpaid laborers from foreign countries, let us create a visa class especially for that. We have visas for skilled workers, such as engineers. Now we'll have one for ditch diggers, too. Who get's to stay longer? I'd say the engineer, since it is far less likely that he'll hurt his back and no longer be able to work.

3) Make sure the line to obtain such a visa begins in the home country only. Granted, embassies effectively are the home country so not everyone is going to high-tail it back to their literal home soil to stand in the line. (A line which should move somewhat faster, provided that (1) can be worked out.)

4) Abolish the minimum wage.
By having a horde of migrant laborers making very little--albeit more than they would have in their home countries--you effectively say "Minimum wage for Our Kind, Dear, but not for you." It would be better to not have a minimum wage at all.

5) Under no circumstances should voting be an option for someone who is here without a visa. Sorry, Democrats: your pool of "victims" to exploit for electoral gain is not going to be replenished by illegal aliens.

6) Take away the employer's "it's too hard" excuse for SSN verification.
The system should take a Social Security Number, a name and a birthdate. The system should return "match" or "no match". An SSN for an "anchor baby" born two years prior won't match the info for the applicant.

7) Come down on employers who still insist on hiring "no match" workers like a ton of bricks.

This still raises further questions:
How do you know if someone has overstaid their visa?
How could it be renewed? Would a trip to the home country be required, or just a hop over to, say, Canada do the trick?
Will we still care about language issues for migrant workers here legally?