My best advice is to contact your insurance company and speak to an adjustor. If you're unsatisfied with the claims payout for your totaled car, you would need to dispute it with your insurance company.
Yes, there are insurance companies that will insure you if you drive for a rideshare company. You will need to have a special endorsement on the policy that allows you to drive for rideshare and you are usually required to have higher limits.
If you have a Named Driver policy, that means the people listed as drivers on the policy are the only ones covered. Since the driver is not listed on the policy, they are not covered to drive the car and the insurance company can deny the claim.
Homeowner's insurance is to repair damage caused by an unforeseen event. In this case, it will most likely not be covered by insurance, especially because it is cosmetic damage caused by home improvements.
So the answer, as you might expect, is a bit complicated. If the insurance company initially set up you up with a rental and it took them 3 months to declare the vehicle a total loss, the insurance company may be responsible for covering the additional 2 months worth of rental charges.