It's been a month of marriage. Having issues with the spouse. How can one annul the marriage in NYC?

This does not appear to be an immigration question.

Can I travel to the USA on my B1/B2 visa now and adjust status to L2 or diversity green card?

First, going from B to L is called a 'change' of status. To go from non-immigrant to immigrant is called an 'adjustment' of status. This is not...

This queation is regarding my H1B ?

Yes, the employer can file for you to start work on October 1, 2020. Be careful about counting unemployment days.

What federal obligations do I have?

This is not an immigration question ... I have re-classified it.

Can I apply for green card (through labour certification process) while in the US on L1 visa?

The employer can file for PERM and, as long as you don't leave the US ... the 60 day ban won't apply to you.

Although living in a different state than your H-1B spouse isn't forbidden, it isn't looked upon favorably. I suggest staying on H-4. With...

Yes, if your DSO agrees to amend the I-20, you can work for a different STEM employer.

Can H4-Ead appy for unemploymnet benefit? does this considered to be public charge?

No it won't be a public charge. Yes, if the EAD hasn't expired, because it is unrestricted and you will be ready-willing-and-able to work...

Should i revoke my h1b?

There is a good chance that you'll get the AOS-based EAD before September. If you ask your employer to 'not' file the papers ... it will...

Can l stay outside of USA more than 6 months? My country is locked down due to Coronavirus

Actually, your greencard isn't at risk until you have been absent from the US for up-to 1 year. The 6 month rule only re-sets the clock for your...