In episode order
Denji is working off a debt he did not take out, for a father who hanged himself, with a chainsaw devil for a dog and no other company.
Devil hunting is a government job. Public Safety runs it, and Makima runs Public Safety's most interesting corner of it.
The Gun Devil is the ultimate threat, killed 1.2 million people in 5 minutes. Its body fragments empower other devils.
A devil's strength is the size of the fear behind it, which is why a chainsaw outranks most of Hell and a marshmallow outranks nothing.
Makima cannot be killed by normal means. She was shot through the head on a train but appeared alive afterward.
Kishibe is the best hunter Public Safety has, and his training method is to attempt murder until the trainee stops being killable.