There is very little mixed use. Majority of the city is zoned single family. The only reason there are no parking minimums is because the California changed that law. It has nothing to do with expanded immigration. LA, despite the immigration, is in massive need of a zoning overhaul to build a vibrant city. Very little is walkable, it is very car-centric, and the zoning is the strong opposition to all of this.
Also, "illegal immigrant" is the term. No human being is inherently illegal.
You seriously think each person who is here illegally is renting or owning their own unit of housing?
The country is not full. But the places with jobs have more renters than rentable units.. which is why a 2br costs $3k a month.
You got 2 out of 3 points completely wrong, and your other was a pedantic point about wording. You should probably slow down and think before discussing this subject.
Immigrants with no particular job in mind look for places where the cost of living is low: they tend to have much worse job prospects than normal, so a minimum wage job in a low cost of living area is better life than double minimum wage in a high cost of living area.
Immigrants often have poor English skills (or whatever the local language is). They often are used to food not common in the country. So if they can find a community of other immigrants that means people they can comfortably talk to, and also makes it more likely that someone can figure out the process of getting food they like into local stores.