If H1-B is picked in lottery, when she can start work. On receipt or she has to wait till H1-B is approved and after Oct 1st.

Sounds like 10/1/16, but would need more facts.

Should I file tax though my US citizen working spouse while my case is in immigration court / removal procedure?

As a general rule, you will want to file a joint return with your spouse, but your question and the facts of your case is/are unclear. If you are...

What is the fastest way I can move to be with him? Meanwhile I want to be able to visit the U.S. To attend my exams.

Schedule a formal consultation with counsel as soon as possible. Many ways to skin the cat, and lots of factors to consider. Really cannot...

Lawyer lack of communication before my individual immigration hearing date

This is an absolute disaster. Try finding another lawyer before your hearing. If you find one, he/she should immediately request a substitution...

May I withdraw petition for immigrant wife but stay married?

You can, but it could adversely impact a future petition/application. You may wish to consult with counsel before taking such an action.

Can immigration come to my house and deport me?

You really should not be relying on Avvo to get this kind of advice. That said, you are subject to having your removal order "reinstated" without...

Is it OK to get a marriage registration in the US even though our religious marriage happened in India a couple of months back ?

As it stands, you do not appear to have a valid marriage for immigration purposes. So, it is indeed advisable to marry in the US. I do not...

Can I stay in USA more than 240 days while H1B extension is in process?

You are misstating the rule somewhat. You are permitted to remain in the US while your extension is pending, but your ability to continue working...

Is it possible to process my green card in any of the EB2 category? Appreciate your inputs.

Very possible, but many, many factors to consider. Employment-based or PERM cases raise numerous complex issues. You should retain experienced...

I really do not understand why so many of my colleagues are advising that your mother is inadmissible. Based on the facts as you have relayed...