Sounds like he is committing unemployment insurance fraud to me.
Yep. “Able and available” is the standard in all 50 states and the territories the last time I checked and I worked at several state unemployment offices for almost two decades.
Fraud would be paying her under the table.
Depends on the state though, here in Florida you can be fired for any reason. Including the boss had a bad day or he needed your salary to make his boat payment.