If you are in an accident in a rental car and you are not listed as the driver, you will be held personally responsible for all costs incurred for both parties. This would apply whether you are At Fault or not!
The mother is liable
As long as this person is listed in the rental contract as driver, yes. However, if you allow someone else drive the car without been listed as driver nad this person gets in an accident, the rental insurance will deny the claim and you will be responsible for all damages.
No he have to listed as a second third or household driver for being cover by insurance
As long as you are listed as a driver on the policy and an accident occurs in a covered vehicle, then yes you will be covered under the terms and conditions of the policy just as any other driver on the policy.
Perhaps. Do you have him listed on the policy as required as a driver. If he lives in your household your policy probably requires you to have him listed as a driver or excluded.
Yes. Some states will not cover an accident if a household member is not listed on the policy.
If the vehicle is titled in both names you may have some liability. Anyone can be sued for anything but whether or not they are liable depends on several issues. If you helped them attain a vehicle as you stated then you may be liable. As far as the policy you should be listed as an additional insured on his insurance and if you live in the same household or ever drive the vehicle you also need to be listed as a driver.
You can be added as a driver if you driver their vehicle sometimes but your vehicle cannot be added to their policy. The policy needs to be in the name of the person who owns the vehicle and all drivers and household residents should be listed on the policy as drivers or just residents. If you put your vehicle on a policy in a friends name the insurance company will deny the claim if an accident occurs. You sign a legal contract and state such in the contract.
It depends, if the policy is a named driver policy and you are not listed as a driver then no you are not covered.
Probably not, unless the friend is specifically listed on the contract as an "authorized driver". Spouses are often included at no charge, but other additional drivers require a fee. I do not recommend ignoring this contractual restriction "just once". If anything happens to the car, the person who rented it is fully liable.
You are still responsible for her and her decisions Legally the owner of the vehicle is going to be held liable.
If you are a licensed driver but not listed on the policy the vehicle will not be covered. If you are not licensed it will be covered.