Yes, if the child born in the US.
No
If the child is a legal citizen they go to the closest legal relative, if there is no one to take the child they go into foster care. If the child is not a legal citizen they will be deported with the parent. If the child is a legal citizen and they aren't registered in school they can be deported with the parent as well.
If you commit a crime, and are not a citizen of the United States, you can be deported, regardless of whether or not your parents are a citizen.
Individuals do not decide whether or not a non citizen qualifies to be deported. Such concerns should be addressed to the Immigration Customs Enforcement agency. (ICE).
The question is a bit vague. I'm assuming that you really mean: Can your spouse be deported if you are a US citizen? The answer is yes. Anyone in violation of immigration laws can be deported. In some cases, the deportation can be stopped if it can be proved that said deportation would cause undue and exceptional hardship on the US citizen spouse or child. This is rare, however. yes, absolutly yes. Get a lawyer.
US Citizens can't be deported from the US. Any alien can be deported.
only if the child isn't a citizen, if he is a citizen then you would have to fly (plane) him over to wherever you live.
The child is an American citizen if the child was born on American soil. The child should be able to stay in the US with the father. Unless the mother takes the child with her. There could be a custody dispute between the mother and father, it should be what is best for the child.
If the child was born on American soil, the child is a legal citizen. The child then has the option of staying, be it a very poor option.
I believe that if your child is a US citizen you cannot be deported. You need a lawyer.
The CitiZen Chil will be adopted by Federal / State
Not a lot. She can still be deported - and separated from her child if the father / government chooses. Either get yourself married or gather up your child and return to your native country.