It appears that your employer is not using an immigration lawyer. If they were, he/she, would have told them that this was a bad idea. Insist...

no No NO!!! You can not be self-employed on F-1 ... unless your DSO approved, and CIS issued, you a 'hardship' EAD.

Filing unemployment as an International Student?

Although the chances are high that he'll be denied, if he has an unrestricted EAD, he might get paid.

I'm a pending asylum but still less than 150 can I apply for SSN now?

Sorry, unfortunately, the system is designed to make it difficult for people that enter the US with non-immigrant visas and apply for...

You didn't tell us your current status nor verify that you got a visa at a US consulate after returning home. Plus, the J has a grace period ......

Assuming that your asylum application is approved, you will be OK.

Possible? Yes Does she qualify? It depends on several factors ... talk to the company's immigration attorney.

Renewal and use of National passport as LPR based acquired through Asylum?

You are wise to be concerned. As my colleague Mr. Berman pointed out, to terminate your greencard for this reason it very rare. BUT .. to be...

You forgot to tell us when/if you stopped working for A and whether or not you started working for B with nothing more than a receipt.

I agree with your lawyer. CIS never reads the cover letters.