so the stretchy yellow dog believed his powers to be magic, while the princess suggest that it's actually just a mutation. neither of these are true, what actually happened was that his dad got infected with alien eggs and gave birth to him out of his head which makes him half alien half dog and thats where the powers come from. this isnt revealed until way later on and his alien dad eventually comes back into the fold to give him an identity crisis.
the princess made out of candy actually is sort of a mutant. she was born from a giant mutated wad of gum called the "mother gum"- it came into creation during the war from the radiation and such. its a bunch of separate sentient wads of gum all attached to each other, PB just ended up being the first one to drop off from it and gain independence (along with her brother neddy). she eventually grew to be more humanoid, and as a little girl she began to crave community and family (like how things were with everyone in the mother gum). she's also a genius who loves to play god, so she decided to just Make Her Own Family by frankensteining some other wads of gum. she lived happily and created a small community with them, though they eventually decided to try to overthrow her (keep in mind, she was still a little girl) by basically drugging her with "dumb dumb juice" which would make her more subservient. it didnt work. instead they got dosed with it, and got turned into different types of candy. they became the first citizens of her kingdom. from that point on as she "grew up" (loose term bc shes functionally immortal) she would grow her kingdom too. she would be absolutely ruthless about this of course. like a true mad scientist, she doesnt care about ethics, she cares about results. she would do anything it takes to keep her kingdom safe. including war crimes. no, im dead serious, she's violated the geneva convention sooo much. she spies on not only her citizens, but other kingdoms too, and will absolutely resort to sabotage. she's obsessed with keeping order and control. so she keeps her citizens (life that she created) intentionally dumb too. she creates life as science experiments and then discards it (goliad, lemongrab, etc.). characters will straight up call her a dictator. shes NOT a good person but shes quirky about it i guess. shes not morally gray shes morally pink