Alright, after staring into space for a solid minute, I think I understand now.
Those crazy teleports Homura can do. They aren’t teleports. She’s stopping time. It just looked like she teleports from our perspective.
When she killed Kyubey just now with that simple handgun. She stopped time and fired multiple times, making him swiss cheese in a single instant. That’s why all those bullet casings were already on the ground.
Homura is actually good fucking friends with Madoka and has been time-traveling repeatedly until she gets herself in a timeline where Madoka never once becomes a Magical Girl. So they can be friends in peace.
But because of Madoka’s extreme potential, Kyubey hounds her with fervor. And Homura can’t even kill Kyubey because he has “plenty” of other bodies.