Are there any birds that fly a loop or inverted manuver?

i suggest you to see the pairing birds of prey. those livin here - the male brings a piece of prey, a hare, or what. the female catches it, and they fall in a spin, holding the hare with their claws.

I know this is an off topic answer, but birds can actually stall (although it's rare). But they instinctly know to fly downward instantly to regain airspeed.

I've never seen a bird fly inverted before, but I'm sure it is possible.

Short answer. Yes.

You should come out here and watch the eagles when they are mating.

Talk about aerobatics!