Drax talks like a Cockney, because lots of planets have a Brixton. Also, it's funny the way he's super-literal about everything and can't understand metaphors or idioms. Insert Star Lord/Time Lord joke here, and we can get past that.
Drax is an interesting inversion on the stock Cockney fix-it character from 50s-70s British TV. Of course he's a dimwit when it comes to theory but an absolute genius when it comes to tinkered. But it's not because he's a smart guy who never got no education because he grew up poor, it's because he's a highly-educated, upper-class, super-human alien who's just stupid. Which doesn't make any sense, but I didn't say it made sense, just that it was interesting.
After failing some classes, Drax left Gallifrey and traveled the galaxy fixing stuff for money, until the Black Guardian imprisoned him and forced him to fix an evil computer that was secretly part of the Key to Time, until the Doctor reminded him that being good is a thing, and he decided to become a roguish good guy instead of a bad guy. Together with the Doctor, Romana 1, and the magic of friendship, he helped save the galaxy from Thanos.
Drax referred to the Doctor as "Theta Sigma". This prompted decades of fan arguments about whether that's his real name, finally resolved when The Moff revealed that the super secret name of The Doctor is "The Doctor".
Drax was clearly intended to be a one-shot throwaway character, so certain writers in the novels and audios decided that it was incredibly important that we learn everything about his background before becoming relevant or interesting, and about his adventures after he ceased to be interesting. Three guesses whether he was in the Deca clique along with every other Time Lord in the Doctor's generation who's been named on the show.