Does my joint sponsor income have to cover me and my family with his income or only his family and the intended immigrant?

The intended immigrant and his family. Have an immigration review the forms as this form can be confusing.

My question is how long time will take the green cad process considering that i am living in united states with work visa permit

Your mother can to file an I130 to establish her relationship with you. You will however have to wait until a visa available in your preference...

Which set of documents are required for adjustment of status in USCIS?

I suggest talking to a qualified immigration attorney prior to proceeding.

Will my approved TPS status still be valid if I travel abroad with my AP based on pending I-485 when I come back as a parolee?

This is a duplicate posting and has been answered. Please see those responses.

If I get a job, will the H1B transfer process have any adverse implications? What are feasible alternatives?

Your best bet would be to apply for an F1 from abroad.

H1 and H4 extension in parrallel

please talk to the immigration counsel of the employer

Do I need to complete the NVC processing fee if I entered the US with a tourist visa and my I130 is approved.

You would not be dealing with NVC. You would be potentially looking at filing the approved I130 with the I485 and other forms like I765, I131....

What happens if you are in your cap-gap extension but H1B gets denied after processing?

It is when you get your decision. Good luck...

Discuss the matter with a qualified immigration attorney prior to appeal or refiling.

Am I allowed to travel using AP through pending I-485 while the TPS application is still pending? What happens to TPS petition?

Unless your AP is based on the TPS, you will lose it when you leave the country.