Can I apply for H4 COS from H1 in the month of August, While my husband got his H1b approved in the month of July.

I agree with my colleagues. You cannot file for H-4 until October 1st when your husband has a valid H1-B status. Seek guidance from your husband's...

Do I qualify, for the right of Jus Sanguinis, for US citizenship.

It is possible. Consult an immigration attorney.

Am in violation of any immigration laws if i start working before receiving my Work authorization?

Yes you should consult your DSO.

Is it possible for me to apply for green card through hardship or any other way. I am divorced and have a son who is 2 yrs old.

You may be eligible for TPS. Applying for asylum and if granted you can obtain a green card a year later. It is a fast process. However you should...

My sister a US national applied for my US immigration 5 years back. Now I have child with down syndrome who is 3 year old.

There are no additional problems. You sill have at least another 5 years until you are eligible for a green card.

I'm married to a green card holder for over a yr. now and we want to apply for adjust of status for me how long will it take?

It does not appear that you are eligible to adjust status. You will have to wait until your spouse becomes a US citizen.

Will legal separation deny my husband of the green card approval ?

It will definitely have a negative effect on his green card application. Consult an immigration attorney.

Your employer needs to hire an immigration attorney. There are many visas that allow EAD but it will depend on which visa you qualify for.

Is it a problem to change employer during AOS for k-1 fiancé visa? The income is well over poverty guidelines. Thank you

No this should not impact the AOS case but you may need to update the I-864 at the interview.

We submitted additional docs in 3 weeks after our interview. And this is the decision we got. What can u say about this?

Duplicate question see previous response.