This as far as it relates to the parks DS got a defective light up do hickey once and they exchanged it on site. But DD#1 light up princess thingy from a Disney On Ice show broke after a few days and luckily I still had the receipt connected some dots to a contact number and they sent her another one within 2 weeks. Again, IDK if the parks would replace it post visit but the Disney ice show folks were happy to replace it. So, give them a call. DD was 4 at the time and thought that light up toy was her only reason for living so give it shot. It couldn't hurt.
Yes! Look at your receipt and contact them. They should be able to help.
At Disneyland I bought a cute little purse, used it once on the way home. And the clasp broke. I was going to have it replaced but realized if it broke like that with incredibly light use, it was going to break again, so I just got a refund. (and they refunded my return shipping as well)