The tl;dr of most of your questions is that it doesn't matter what happens before Age 761, because Raditz will wipe out the earth, with or without Goku. In these scenarios, Piccolo does not get released by the Pilaf gang because there's no need or opportunity.
I began rewatching the entire series and began with Dragon Ball and will go all the way through Diama. But several question came into my mind.
01) How would the series turn out if Goku just stayed in the wild like he did until he was an adult and meet Bulma then?
- He would not let the Pilaf gang take his grandpa;
--- Pilaf gives up
--------- RR takes Dragon Ball by force (sending Tao if they have to); assuming they're not stopped by Roshi when they come to take his
-------------- Red gains his height and potentially takes over the world
----------------------------- Raditz comes and clears earth
-------------------------------------------- Namek remains unmolested (assuming Raditz never learns of the Dragon Balls)
----------------------------------------------------------------- Buu potentially is resurrected and begins terrorising universe
--- Pilaf takes Dragon Ball and rules world; assuming they're not stopped by Roshi when they come to take his
----------------------------- Raditz comes and takes/kills Goku (if still alive) and clears earth
-------------------------------------------- Namek remains unmolested (assuming Raditz never learns of the Dragon Balls)
----------------------------------------------------------------- Buu potentially is resurrected and begins terrorising universe
02) How would Bulma and Goku work out as a couple?
Probably slightly more stable than Bulma and Vegeta.
03) Is Goku the way he is because of him living in the wild and being away from Civilization?
It depends how you define "way he is". Kind hearted and calm is largely based off his head injury and nurturing from Grandpa Gohan (regardless of DBS Broly's meddling). One could argue he is more innocent because he wasn't exposed to worldy corruption.
But he does have a lot of animalistic tendancies that would certainly come from there.
04) How would Goku turn out if he was never adopted by Son Gohan?
Assuming he never hits his head; he potentially destroys Earth within a couple of full moons well before Age 749 (the year Dragon Ball starts) and is stranded there until Raditz comes for him.
Alternatively, he is stopped by Kami, Korin, Tao or Roshi. The events of Dragon Ball can largely play out similarly until Age 761 depending on whether Goku is stopped or killed. Supposing Tao doesn't kill Goku, Goku might be more inclined to go with Raditz if recruited... otherwise, Raditz will kill Goku and Piccolo won't be there to help.
05) If Krillin is a monk, then how was he able to have a kid when monk's take a vow of celibacy?
Considering he stopped shaving his head, I think he abandoned that vow, probably the minute he left Orin Temple.
