Obviously these are farcical questions but the museums answers are likely not to be so laughable or ridiculous. Quite a lot of their answers will show they don’t actually own the item - they just have it. For now.
In reality the museum is just the current holder of something that was probably actually stolen. A thief can’t claim much of anything can they?
Perhaps the museum should clarify its exact claim so that no others can challenge them. And “because we’ve had it for awhile” doesn’t count. Maybe the museum should not only admit they don’t have copyright but that in a very real way they shouldn’t even have it to begin with.