I am afraid that can be found a violation of your status since Au Pair J1 is for cultural exchange, study and assistance to the family in exchange...

Who long would it take for me to get a work permit?

I would contact USCIS. Work permits now do take longer, but that seems to be a little too long.

Can asylee dependent who is studying in the country -Nepal that claimed "fear of persecution” can do back and forth to USA ?

I think the family should consult with an Immigration attorney. The problem is cases like this is that if it is safe for the dependent to go back...

ITS BEEN MORE THAN 7 MONTHS SINCE I REAPPLIED FOR WORK PERMIT SINCE I LOST IT.

You should contact USCIS and inquire about the status of your application.

Can I sue my employer for wrongful termination ? For bringing a dangerous situation to a superiors attention.

You should consult with an attorney. Threats of bodily harm, etc. can also be reported to the police.

I doubt any attorney will agree to such a limited involvement on such short notice. Here is how to write a rebuttal: You will use "caption" the...

Working without a break?

Unfortunately, there is no law about special "holiday pay". If you are a Union worker, you should voice your concerns with the Union. But it seems...

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Do I have to prove that I stayed at my home country before applying to cr1?

One has to fulfill 2 -year residency requirement in their home country. Most likely, you will have to show that. You should consult with an attorney.

I applied for I 589 dated on 1st Nov 2019 but there is no acknowledgment receipt came ?

Do you have a tracking number? If you will not get any confirmation, you most likely will have to refile. You should consult with an attorney.

Perhaps, there is a mistake somewhere. You should work with an attorney to clear it up.