Does anyone know if this new collection folder will possibly include 13* eggs? I heard JP has something similar for getting 13* eggs, but I don't know if they're specifically from the collection folder or a different system entirely.

The 13* Egg Collection Folder is a separate, permanent Collection Folder set on the JPN server. The new Collection Folder we are getting seems to be the equivalent of the very first one from the JPN server which was just Revolsio weapons, though until it actually comes out, we won't know for sure if it includes Eggs or not.