Illegal Alien Financial Support

Here is a letter (via the web) that I sent to my senator from Missouri, Claire McCaskill:

I am hearing many stories these days about illegals getting money from our government and also getting free health care and subsistence. Examples:
(1) If an immigrant is over 65, they can apply for SSI and Medicaid and get more than a woman on Social Security, who worked from 1944 until 2004.
(2) Florida ER doctor: "I live and work in a state overrun with illegals. They make more money having kids than we earn working full-time. Today I had a 25-year old with 8 kids -- that’s right 8; all illegal anchor babies and she had the nicest nails, cell phone, hand bag, clothing, etc. She makes about $1,500 monthly for each; you do the math."

So, the question is, "Do illegal aliens receive government subsidies, taxpayer money and other free assistance?" If so, why?