(1) it's possible to reconcile the idea that the demand for labor is inelastic (so that raising the minimum wage does not significantly decrease employment) with the view that the inflow of immigrants doesn't affect wages much. (In, theory, for a given inelastic demand curve, a small shift in supply should cause a significant fall in wages.) The inflow of immigrants could also increase demand (shift the demand curve). The rise in the number of immigrants could easily create greater demand for services for immigrants.
(2) more importantly, whether or not there is immigration, the wages of unskilled (or rather, uncredentialed) workers will be depressed by (a) trade competition with low-wage workers abroad; and (b) the mobility of capital to places where low-wage workers can be hired.
(3) the idea that immigration drives up housing prices makes sense for the rental market but not for the owned-house market. Immigrants typically don't buy houses. But rents have been falling behind purchase prices. Or at least that's what the data that Dean Baker presented indicate. -- Jim Devine / "There can be no real individual freedom in the presence of economic insecurity." -- Chester Bowles