Good question. Probably keep it for a while, research it and then play it by ear. Let's just hope it isn't cursed!
Depends what kind of relic.
No , I would do some research on it . Find out the time line it belongs to and then ba<x>sed on the importance I would judge .<br />
If it was important donate it , other wise put it on Ebay .
You would possibly need to get it looked at to be sure its a relic, and if you did that then the museum would probably hear about it and steal it from you.