When we need to apply for I-751 application?

You can file 90 days before green card expires.

Can he be deported

It is possible for anyone who is living in the US without permission to be deported.

Doubtful unless she has attained residency requirements of one of the states which would allow her to come under the jurisdiction of a state court....

Who should sign G-325A forms?

The G-325A form is signed by each respective person.

Given my physical and family situation, is there anyway to file for immigration legalization now & how?

There are no provisions available for getting immigration status due to a disease. Humanitarian visa for entering US for necessary treatment is...

Can I file a lawsuit or a small court case against American Airlines. What other options do I have.

Lawsuit issues of this nature are not immigration issues. You may wish to repost.

Can my son Petition for his 16 year old wife?

Assuming your son has status and legally married he can apply for his spouse. However because he is 18 he will someone else to file the affidavit...

Can the daughter file a petition to get her dad the green card faster or can i file for him fast so the family will be tighter.

She cannot file for him until she turns 21 years. That would be faster because priority dates for siblings are much longer.

Secondary education in the US is high school.

He has no police record , he is clean on everything

Because he is here illegally he will have to go through a waiver process and prove extreme hardship....I-601A, then process in home country. Tough...