What is the best possible way to extend H4 visa?

Traveling back to India is not a bad idea assuming you don't have any bars to admissibility.

After taking all the necessary steps, if the EAD is actually lost, you can request for reissuance.

Can I stay beyond I-94 expiry date ( Aug,30 2016)

Yes you can stay in the US legally until a decision is made on your I-485 petition even if your I-94 expires.

Can I remain in the US and apply for adjustment status if I am here with an ESTA visa while an I 130 is pending?

You cannot legally wait in the US and also you cannot apply for adjustment of status.

MY BOYFRIEND HAS BEEN IN THE STATES FOR ABOUT 9 YRS ILLGEALLY AND WE ARE IN THE PROCESS OF GETTING HIS IMMIGRATION PAPERS

As my colleagues precisely pointed out, you boyfriend need to divorce his wife in Mexico to legally marry you here. Then you can file I-130...

How do I obtain a Visa since I'm a non-immigrant? Can I go to Mexico real quick and get a brand new i94?

I-94 is generally traceable from government record and try to put an effort is that direction. But I don't see how your I-94 will be helpful here.

Do we need to report to USCIS if our H1-b approved employee switch client project even though staying on our(same comp) payroll?

You are asking a very specific question and it is better you speak with your attorney.

It's perfectly normal because the two cases are processed separately. Follow your wife's status at the USCIS page if there is any update....

Hello I just got married to a us citzen What's the process of starting my greencard

Please talk to a local immigration attorney. Assuming you're in the US, your current immigration status and your immigration history are relevant....

Can I file an I-130 for my husband?

You can file for I-130. But the facts you stated trigger many immigration bars. Even if the I-130 is approved, he cannot get a visa to come to the...