Theories, therefore not put in spoilers
1. All members of the Imperial family are reincarnators. That would explain why they are such prodigies and one of the reasons for the "manifestation." The only reason they aren't "prodigies" is the prior abuse and lack of instruction earlier.
2. Dude under the tree is definitely a guardian, as is the fox on the intro page.
3. They can only use their powers when they are together.