The employer can file a petition for you, yes.

How can I get the legal guardianship and the physical custody of an abandoned illegal immigrant child residing in USA?

Yes, you could do an application for a juvenile court dependent.

My VISA extension is in progress with my current employer. I have an another offer in Y company, Shall I start the VISA transfer

It really depends what kind of visa you are on now, and what kind of visa your new employer is filing.

I have been ordered removed ,will applying for an I-212 waiver help?

What are you waiving? If you have no legal basis to be in the U.S., filing a waiver will not get you an immigrant visa.

Three months is not a long wait at all, and the fact that your wife got scheduled before you is not an adequate basis to get your case expedited.

Is it ok to be out of payroll for a month soon after GC approval?

The issue is whether there really was a job for you when you got the green card. If there was, you are fine. Rule of thumb is to work for the ...

We had our aos interview for less than 10 mins. of basic questions, no decision yet after interview. Is this a good sign ?

It depends on what evidence was in your file.

Yes, you can get a stamp if you are approved.

Is it advisable to Travel outside USA on a Buisiness trip , have an L1B Approved Visa?

Not a problem but you need a new visa to return to the US

I want to withdraw my asylum case In us but i dont want to come back in my home country?

The U.S. will not prevent you from travelling out of the U.S. to any country you choose.