Yes it is possible. As long as their criminal record is clean, legal Immigration status can be validated, you're ok.
"My aunt became a legal permanent resident of the United States after receiving her green card."
No, marrying a US citizen or a permanent resident does not grant the illegal immigrant legal status regardless of whether there is a child involved or not.
no, only us citizen can help for permanent resident
yes
no
no
If the child is a legal resident of Mexico, that is where an order for child support is filed.
I am pretty sure that might depend on the country - I don't think all countries have identical laws in this respect.
No..but the child can be adopted by a natural guardian
yes. it can, but not always is.
yes you can when the child turns 21 you can file for your papers
No! If the child is born in another country and not on a military base, the child is a citizen of the country to wit it is born in. The parent will have to fill the proper paperwork to get the child it's US status.