Yes you can- but remember that the ability to marry an illegal is SEPARATE from whether or not that illegal will ultimately be able to get legal status due to that marriage.
This issue is a "Catch-22" in that there are not laws prohibiting a illegal foreign national from marrying a U.S. citizen. However, the person must have the required documentation when applying for...
That's not possible.
Furthermore, the US has very strict laws concerning relationships between minors and adults, and many jurisdictions agressively enforce such laws.
"He/she will have his/her butt kicked out of the country, unless he/she can claim being a victim of domestic abuse or something like that." This is not true, it all depends on how long you've been in...