How can I make my H1B extension filing case strong so that it doesn't get a denial?

First, you need a Board Certified immigration attorney. Second, you need the correct responses to the RFE which you will almost certainly receive...

What financial documents do I have to submit to NVC?

What you really need to address is the rule that you must be living in the US and establish domicile several months before his interview at thUS...

When can I work and study at the same time?

In theory, you can work when you get the EAD but that also depends on what type of green card case you have filed, how it was filed, what evidence...

Can i travel to INDIA when my H1B is in process , Currently i am on OPT Extension with valid work permit card in my hand?

Traveling before the approval of the H-1 and before Oct 1 is a horrible. I would hope that your attorney told you this also, and if so, you should...

When will my applications be approved?

You definitely have issues. You should either consult a Board Certified Immigration attorney or call Senator John Cornyn's office in Dallas to ask...

H1B Extension in process and possibility of traveling back to home country?

You need to discuss this with your attorney; the one who is being paid to represent you. Specifically, as the attorney about the "last action rule".

L1B Extension

This has already been answered and you should be speaking with your attorney anyway.

In this situation children have nothing to do with the case.

I have PERM Approved in EB2 but I do not have degree certificate

Is the attysaying it will get rejected, the same attorney who created the labor certification?

Yes you can challenge the refusal. Why aren’t your company and your attorney helping with this?