No, not by merely having a child born in the U.S. However, when the child turns 21, the child may file a petition for their parent. But before that, the parent always run the risk of being arrested and deported, even if they have U.S. citizen children.
It is not impossible to get a green card (permanent residence) in the circumstances you describe. However, it will be extremely difficult. The fact you were illegal (and deported) means you will have to apply at the US consulate in which you reside. The application procedure is long and costly this way-you will have to attend several appointments for medical exams, biometrics and interviews. If you apply in the US, whilst residing illegally, your application will immediately be rejected and you will be deported again. I would advise against doing this because it could affect the residency status of your wife-she would be committing a felony for harboring you and sponsoring your petition. I would advise you and your wife apply for residency in the country in which you live. But like I stated, it is very difficult to get permanent residency (green card) once you have been deported and entered the country illegally. In fact it is very difficult to enter the US even temporarily (visitor) if you have been deported. The only occasions I have seen concessions made have been for asylum or with people able to invest around a million dollars.
if you married a us citizen then you should be a citizen too.
No, must correct the illegal status first.
Does have marriage, children, work history in USA going for him.
I would not leave the USA for any reason, might be refused entry
The illegal partner will probably be repatriated to his/her home country or be imprisioned prior to deportation. The American citizen may be fined or criminally charged.
Illegal entrants are subject to deportation.
There is no risk for deportation based on your illegal status. However, you are STILL at RISK of deportation if you commit a serious crime or crime of moral turpitude while you are a green card holder. You would be deported after serving any prison time.
It is possible for a U.S. citizen to marry an illegal immigrant if the immigrant has valid identification. However, marrying a citizen does not automatically confer permanent resident status or citizenship and is not a guarantee that the person will not face deportation. Such situations are assessed by the USCIS on an individual basis, for more information visit the United States Citizenship and Immigration Services website at http://www.uscis.gov
no, only us citizen can help for permanent resident
This is not a question.
It is possible for a non-US citizen to go to court in a custody case for a child. If one party is an illegal immigrant, they may be subject to deportation.
First, there's no such thing as an illegal citizen. Second, there's no such thing as an alternative lifestyle. But if you are asking if a marriage between a gay person and an illegal immigrant of the opposite sex would be valid if it is not consummated, that depends upon the laws of the state where the marriage took place. If the marriage was made with the intent for the illegal alien to gain citizenship or permanent resident status, that won't happen. Marrying a U.S. citizen DOES NOT automatically confer citizenship or permanent resident status.
Yes.
by legally marrying that us citizen or print a form from the internet requesting to be a permanent resident
Yes.
Deportation.