While bede is adopted by opal not too long after, he does get the boot by chairman rose because... reasons. ( the game does not make it clear what bede did, other than moderate vandalism, which chairman rose wanted)
Pokemon is all about battles between animals, and your party can get hurt or faint. There are no story elements depicting an animal getting hurt otherwise, but one pokemon does crash into a gate near the beginning of the game. It is not shown to be injured.
Many parallels have been drawn between Pokemon and dog-fighting over the years, but injuries are never shown and just as much emphasis is placed on treating Pokemon with care and respect.