After H1B COS approval, say employer agrees for reasonable delay to join, how long can be that delay?

Once the COS is approved, you are to join your H-1B employer. Not doing so is violating status granted you by the USCIS.

Do I have to travel with principal applicant( My husband on H1B) from our home country (India) to USA if we have new I-797 ?

You can return to the U.S. on a valid H-4 visa.

H1b to b2 approved; is b2 in passport valid for future use?

He should not have a problem entering on B-2.

Say H1B (COS from H4) is approved on Jan4, how many days can i wait before I join the job?

You should join the company to maintain status.

I strongly recommend consulting with an experienced immigration attorney before you file any applications. In your case, I will go a step further...

How to convince VO with different salaries appearing in Offer letter and LCA.

This discrepancy could be an issue at the visa interview. Also, you have not mentioned how much you are actually paid. The VO may ask to see pay...

Can I still apply for H1B amendment .Do the current LCA will still be valid ?

I'd advise the company to file for the amendment if the original petition was filed with work location X. It is not unusual for the Consulate to...

Can I re -enter USA with valid H1B

As long as you are traveling within the validity period of the H-1B visa you should be OK. Carry proof of employment for POE verification.

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What steps do i take so my employer gives me the pay slip and i can cos from H1b to h4 .

H-1B is for bona employment. It is not unusual for Consulates to deny visa if they conclude that you were aware you are not working and not...

Can I marry my European Fiance traveling to the United States on ESTA visa if we plan to live abroad after marriage?

If he is already in the U.S., you decide to marry and he timely departs, I don't believe he will be violating his status. Pre-conceived intent...