I am a US citizen and I need to petition for my mother to come to US. What documents do I need to supply?

Depending on her country of origin, it will probably take 9-18 months. You will need your birth certificate, proof of US citizenship and her...

You should be eligible to file for adjustment of status to the green card without departing the US.

The "Alien Number" would be expressed as "A# xxx-xxx-xxx.

Does a denied change of status, cancel my B2 visa?

It should not automatically be cancelled, depending on the timing of when you file for the COS and other factors.

Traveling during H-1B COE

This is a sensitive type of issue that is best addressed to the employer's immigration counsel.

I'm the owner of the company that has obtained the E1 status. Can my wife (e1 status also) work with me without the EAD?

It is not difficult to obtain the EAD, so I would recommend that she obtain one to avoid any problems.

Adjustment of status

You better amend your response to that question at the interview and present a certified copy of any court disposition of the case.

I applied for solo I-212 why is taking so long??

It can take several months for the USCIS to adjudicate an I-212, depending on the office location.

H1B Lottery

Yes, they should be notifying petitioners whether their filings we accepted in advance of that date.

I've been denied an O-1 visa once. I want to go next year to study in a F-1. During that time, can I apply to an O-1?

It is possible to apply for a change of status to O-1 from another category, such as F-1, after admission into the US.