I need a car for only four days out of every week. Do I still havevto provide proof of my own liability insurance.

Yes

No... however if you have the type of insurance that does covers a rental car that doesn't present a problem or you have the option of using what they call ldw insurance that they have which is limited damage waiver it's your choice with limited damage waiver Thrifty provide fat but you have to pay for it per day

They should have there own