Does renters insurance cover damages to garage door?

Answer 1

No, your tenants policy will only cover your contents. Unless you are negligent in the garage door being damaged, like you drove into it. Then yes it would be covered under your liability coverage but the homeowner would still need to go through his insurance company and subrogate against yours, most insurance companies do not work directly with the third party and rather deal with another insurance company. More specifics regarding the damage and how it happened would be required to assess as well as your policy wording, I suggest calling your insurance company and discussing it with there claims office, most insurance companies will have some sort of claims guarantee where they will consult you on the claim before making it affect you.