Can a auto insurance company ask for proof of repair from hail. from 2 years ago from a different insurance company?

As to auto insurance, the insurer will not offer physical damage coverage on a vehicle that currently has damage. And they surely should not have to pay for a claim that was already paid for two years ago.

Insurers may have access to a centralized claims registry, at least as to claims that resulted in significant damage and therefore, great repair expense.

A new insurer is not responsible for damage that occurred before its policy went into force. Therefore, it will want to know the condition of the property as of the effective date of its policy. This is usually done by having an inspection of the property done, usually at the insurer's expense. Part of that inspection will likely involve questions about prior damage.

It is important to be truthful in the answers. The insurance company bases its decision to insure and the premium that it charges, based on its assessment of the risk. This includes these kinds of questions. If the answers are not truthful, the insured runs the risk of the insurer canceling the policy based upon "material misrepresentations". A material misrepresentation is a misrepresentation that the insured relied upon to its detriment by issuing a policy that it would not have issued, or charging a premium lower than it would have charged had it known the truth.