If there are 12 million illegals in the United States, that would be less than 4% of the total. Hardly enough to affect employment of citizens.

There are many groups contributing to the illegal total; estimates of Salvadorans range up to 2 million, many illegal. Latin Americans exclusive of Mexico are about 25% of the total.
Many illegals from eastern Asia simply are not counted because they disappear into a society which lives and works together. Estimates are 10% but this is probably low.
I haven't looked into this to any extent; just quote Wikipedia and similar estimates.

It is impossible to estimate the number of illegals paying federal and state taxes because these figures are confidential, but I would guess that the majority contribute since nearly all are on payrolls of some kind. The few not declaring probably would be mostly domestic help.