Change of status from OPT (F1) to B1/B2

It will depend on the CBP officer you meet at the border.

Asylum

The only way to receive updates on a pending asylum case is to go to the office where you had your interview and inquire in person.

I am on F1, asylum pending and my employer ready to file my Green Card?

If your employer will be filing for your green card and once that priority date is current and your F1 expired, you will not be able to receive an...

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Can I

You can find out what you need to apply at a local Social Security office.

You can come in to the asylum officer where you had your interview and inquire regarding your status.

STEM OPT Extension

Your employer needs to read regulations regarding OPT employment and e-verification. Or, you can consult with an attorney and inform them.

My husband entered USA when his i-730 approved .I am an asylum and petitions him . We fill I-485 form for him but as a refugee

It should not be a huge issue, and it is "fixable" in any event.

Do i need to apply for a Re entry permit Form I131?

It is likely correct. re-entry permit application can be found at uscis.gov form I 131.

Child support law for impregnating a woman on a student visa in the US

There is no difference. Your child is your child.

Can I travel by airplane from new jersey to california

You may travel via plane. You should have on you proof of your asylum filing.