If your daughter is listed on your insurance policy and a premium is being collected for her, then she can use your insurance. If not, she will need to use her insurance policy at work.
If you were involved in an accident with this person then their insurance information will be listed on the accident report. If you were not involved in an accident then it is not your business who they have insurance with. Much of this is covered by the privacy laws so if you really have to know ask the person.
You don't have to live there as long as you are listed on the policy.
Probably not, as most policies only cover drivers not listed on the policy if they were given permission to drive. If you gave your unlicensed daughter permission to drive, then you can be issued a ticket. However, if the accident was not your daughter's fault, then the at fault party is responsible for the damage they caused to your vehicle, regardless if the other party was licensed or not.
No he have to listed as a second third or household driver for being cover by insurance
The names of the "insured" on the declarations page of the insurance policy and those listed as "other operateors" of the vehicle list on the same "deck page" of the policy are covered. Liabilites and their limits are listed in the policy.
Parent's policy pays
You do not have to live with them as long as you are listed on the policy.
Yes. Some states will not cover an accident if a household member is not listed on the policy.
Your insurance won't pay for any damage or injury to persons or vehicle. (unless they were driving legally with a drivers permit)
First, you cannot find out what insurance company another person uses as this is a privacy issue. If you have had an accident with this person, the insurance company will be listed on the accident report. This is your only option for getting the insurance company name, unless the person wishes to tell you.
If there is a lawsuit, they will name the owner of the vehicle, your insurance company would more than likely represent you/your daughter. I do not think you can be held liable personally.