Popee was the result of a one night stand.
This is why Popee refused to believe Papi is his real father. He know his mother(I headcanon her to be a very wealthy but promiscuous singer) had slept with many men before and think one of them must be his real father not Papi. When Popee was born, His mother don’t want to raised him and instead hired a nanny to look after him. Years later, his mother meet up with Papi again and that when Papi find out he had a son from his fling. He decided to took Popee under his wing. The White wolf is actually an evil cult.
The white wolf cult who are hellbent in bringing the apocalypse to end the universe. They spend years searching for someone who is the key to the Awakening of their god(White wolf, duh) that could destroy the universe. Guess who is the one fated to awaken the white wolf? The White Wolf is Kedamono's mother.
This is now canon. While Ryuji Masuda originally stated this theory is false, Wakako Masuda has since confirmed it is true. Basically, the theory stemmed from how Kedamono is terrified when he sees the white wolf rise up in the final episode, "FACE." With this in mind, combined with the fact that the frog says, "Kedamono's face... looks like his mothers." implies that the white wolf resembles Kedamono's trauma stemming from his mother.- Alternatively, the white Wolf was not Kedamono’s mother but could be the deity that Kedamono’s mother(who is the leader of the white Wolf cult) worshipped.
They are out in the desert by choice.
The circus is clearly more dangerous than it appears with how psychotic Popee is and how often their misadventures result in someone’s death. At some point they tried performing for real people but accidents occurred resulting in casualties. They were run out of town and eventually forced to make their new home in the desert performing for a made up audience. Popee is autistic.
He has a hard time thinking of others and doesn't seem to realize what a lot of their body language means. He has an exceptionally low response to pain, unusual movements, and seeks repetition. He gets very easily agitated and enters fits of aggression and childish behavior. Word of God says he hates hugs.