Does NASA purchase insurance on its spacecraft?

The government is insured by YOU, the taxpayer. Why would they buy insurance from a filthy rich corporation when they've you poor little ol' you to fall back on?

No, the government does not (generally) buy insurance, and NASA is part of the US government. But ... sometimes the spacecraft still belongs to the manufacturer, and the gov't has not yet taken ownership. It that case, the manufacturer might have insurance. I think (not 100% sure) the contractor is New Mexico State University

The US gov't is its own insurance company.

No, government agencies rarely use insurances, this also applies to space flight. Commercial satellites are insured usually, as part of the launch service package. Insurance companies don't like unknown stuff, and most government spaceflight is full of unknown things for the insurance mathematicians...contrary to commercial launchers, which quickly get confidence.