I'm sorry for not having more time to fully research this, but here's a short answer.
Many satellites don't have any ongoing insurance of any kind. Some countries require short-term insurance to cover liability incidents during launch, deployment, and initial operation, but generally there is no legal requirement to keep long-term insurance.
Those satellites that do have long-term insurance are insured against loss of function; that is, it's a business decision, where the operators want to protect against the chance that they might lose the ability to make money off the satellite. This protects the operator, but doesn't cover liability or damage the satellite might theoretically cause to other operators with other satellites.
For the most part, the only "insurance" of a sort regarding liability for damage caused by space operations is the liability provisions of the Outer Space Treaty and the Liability Convention, which say that the launching state(s) will be responsible if there is fault that results in damage in space, or responsible for all damage caused on land.
I'm not aware of a list of insured satellites, but it's possible that someone in the industry has one. There are a few companies that insure satellites though, so I don't know who exactly would compile that.