if someone is inadmissible to the U.S. under 6C1 can he/she enter the U.S on an approved advance parole (I-131)? Please advise.

Will be entirely up to the CBP whether to admit you on AP or not.

Can i raise a file to the EU or USA court against my own country and government ?

Please try and let us know how it went.

Will need to explain what happened. There are different ways of doing that.

Will I be able to exit and come back into the US while my green card renewal application is processed?

Yes - upon attending your biometrics appointment you will receive a stamp extending the validity of the GC for an additional time and can travel on...

What happens if you could not renew you visa because of COVID?

You had the responsibility/obligation to timely file for either extension or COS. COVID did not excuse that. Now seek to depart before accrue...

Since already have a lawyer, pose these questions to your lawyer/s. They are paid for that.

Immigration H1B Problem?

You need to depart ASAP and apply for your visa abroad. Once the visa ban is lifted, that is.

Planning to apply for H4 EAD with H4 pending

Go ahead and apply for the EAD as well. Am surprised did not do it at the same time as applying for the H-4 itself.

This will be illegal employment and could land you in removal proceedings.

Can my partner earn royalties on Youtube while waiting for EAD?

I agree. Can continue receiving royalties from outside the country.