Connecticut

Typically, no. You don't want liability only because the car will not be sufficiently protected.

The car can only be registered by the owner. If you sign the title over to someone else, they will own the car and can register the car in their name.

My condolences. Yes, you can and should add the car to your policy.

No, since you will be driving your parent's car, they will need to add you to their policy. There are a few reasons.

Yes, there are several companies that will insure you with a learner's permit. Not all companies will do it but most will.

Connecticut does have a subrogation law which states you "are entitled to a comparable rental vehicle or reasonable compensation, for a reasonable period of time necessary to settle your claim or repair your vehicle." However, because you do not know who the individual is, I am not sure how would be the party to compensate you. Normally, you would need your rental reimbursement coverage.

Yes. Your ex-wife can insure the vehicle as long as you are listed on the policy as a driver (because you are the one financing the vehicle) and listed as the additional interest since you have a financial stake in the vehicle.

There's a couple of things to think about here. Does your daughter live with you?

There are car insurance companies that will insure salvaged vehicles but there aren't as available as vehicles that haven't been totaled and repaired. Also, you might end up paying more in premium for what the insurance company sees as an additional risk.

The answer would depend on where you live or park your vehicle the majority of the time. If you live with your boyfriend, you should be able to be added to his policy.