Here is info about babidi's mind control

Babidi tries to manipulate other people's minds so they obey babidi.He also tries to revive Majin Buu.
The first person to refuse babidi's orders was Vegeta.
Babidis best henchmen is Dabura.

Majin Vegeta

Vegeta's transformination to majin was little different.
He wanted to be majin so he could be powerful like he was before.After Vegeta transformed he starts to shoot people in the stadium because Goku didn't want to fight with Vegeta.After that Goku had no choise but to fight.

After Vegeta had fought with Goku Majin Buu was born.
I don't know specific why Vegeta goed to kill Majin Buu.
Anyway first he shot Atomic Blast through Majin Buu's stomach then Buu regenerates.When Vegeta noticed that Buu won't die he hugs Trunks and the hits him and Goten to the ground and Vegeta tries to kill Buu by blowing himself.