Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
Use of a free-day or dollars-off coupon might void the free coverage provided by a Visa card. If the OP is planning to use such a coupon, it would be wise to check with the card's insurance administrator first, and get a written response, perhaps by Email.
As to third-party liability coverage, if a renter does not own a car, options include: 1) paying the rental company's daily fee for supplemental liability insurance (SLI); purchasing a non-owned automobile liability policy (mine costs $154/year from The Travelers); or finding an insurer whose home insurance policy covers third-party liability when driving rentals (Chubb offers such coverage, I believe).
Regarding loss of use/diminution of value, individual states might regulate a rental company's right to collect these charges.