H1B just got laid off - grace period?

The good news is that you may within the grace period(60 days) find an employer to sponsor you. Is there an I-140 pending? Can you file a change...

Green card eligibility

Yes, you may apply for your spouse, your children so long as they are unmarried.

Is necessary cancel my asylum petition if I get married with a citizen?

Obviously you have some unanswered questions and i suggest that you consult with one of us on avvo.

It is too hard to tell. Call customer service or check your status on line ..go to www.uscis.gov/status

How Can I emigrate to the United States

Only immediate relatives can help filing an immigrant petition, your cousin cannot do anything there. Depends on the treaty between your country...

Could I travel abroad and re enter US while H1b petition is in process?

You need to readdress your issue or meet privately with an attorney.

Can we file H4 EAD while waiting for H1B approval

It doesn't appear that you are eligible for the I=140 EAD unless you have a current priority and may also apply for adjustment of status.

Is it easy to change from H1 to J1

My steamed colleague already answered you, however, you may also consider consulting with an attorney about other possibilities.

Would i be considered illegal?

You will not be an illigal and you may proceed with citizenship. However, you may need to renew your card for your employment purpose as it takes...

What can I do?

The question is why did she lie? If her green card was issued based on fraud..then she is not a permanent resident under the law and regulation. ...