If the Down syndrome child was born in the U.S. the parent MAY be qualified to remain in the country to care for it as long as the child remains in their custody. However, if the baby was not an "anchor baby" - no.
get a green card or a visa..
No he cannot
Yes because if not you would be considered an illegal immigrant and you would be sent immediately back to where you came from. Green cards are for citizenship
Well the baby is a U.S. Citizen and since the baby is a U.S. Citizen, in time the "illegal immigrant" may be able to get a green card and first of all an illegal immigrant isn't illegal if they have a visa, except if they were living and working in the U.S on a tourist visa,
An immigrant who is unlawfully within the US is not eligible for permanent residence status (green card).
If you are married, you can apply for divorce.
I doubt an illegal alien could even join the military, let alone get a green card. A illegal immigrant could not become a member of the US military, nor can an illegal immigrant obtain legal status under the current immigration laws. All foreign nationals who are unlawfully present within the US are subject to deportation when taken into custody by immigration authorities. Exceptions are made in individual cases, if the immigrant qualifies as an asylee or refugee.
Absolutely not, don't even think about it.
the US citizen shouldn't
My guess is no. You have to prove that you have a real marriage to stay.
The marriage license would not be valid, but he could also get a green cars because he's married to you.
Legally, no. In practice... even an undocumented (i.e. illegal) immigrant could probably vote in LA.