I don't work for Disney so I can't say for 100% certainty, but I do work in the industry so I have some knowledge. For Mickey and the Magical Map, the main songs are sung live - by Pocahantas, Mulan, and Rapunzel. Those would be live (and you can see their mics). But the background vocals are I'm sure prerecorded, so the dancers would be lip syncing. It's similar to how it is on cruise ships. I'm not sure if that's very clear.
Basically, if it's one person singing, it's live. If it's many people singing it's prerecorded.