Can H1B reinstated after 6yrs of its expiry from a current H4

No Your employer needs to retain an experienced immigration lawyer to review all the facts, advise them, and handle the case. Your employer can...

How long will a lawsuit against USCIS take? On average , how many months will it take for them to respond?

There is no average for lawsuits. I have handled one that was resolved in three days, and several that took well over a year.

Can a H1b visa holder while working full time for the petitioner, also volunteer for another for-profit LLC as an advisor?

No, that would be considered unlawful employment.

Can a step parent sponsor a step child who is already over the age of 18 years

Only if the step-parent relationship began while the child was under 18. You should retain an experienced immigration lawyer to review all the...

If I-539 is denied, will the current status expire? Do adjudicators indicate that you must leave in the denial notice?

Ask your immigration lawyer.

---> Now how long can I stay in the USA to find new employment?

You cannot. H-1B status ends with the H-1B job and there is no grace period. Upon the H-1b status ending, you begin accruing unlawful presence.

The immigration consequences of convictions depend on the exact language of the statute under which the conviction took place. You need to...

Visa appointment went smooth but put on administrative processing!?

Security and background checks. Yes, it can potentially take years.

Does a trip aboard of over six months and less than one year, wipe out the entire previous continuous residence?

If USCIS determines it interrupted continuous residence, then yes.

It is necessary to have full custody over my children's to they get approved for green card?

They must have the consent of the other parent to immigrate. You should retain an experienced immigration lawyer to review all the facts, advise...