Edit Footage Based on Camera Data / Camera Metadata?

Hi. I have no experience with self-made movies, but would like to know: Do film clips (of all currently used file formats) include camera metadata like camera model, lens model, aperture and such? If yes, which file formats (cameras) do you know of?

If yes, is there any video editing software making use of this metadata, maybe correcting typical lens distortions and vignetting if the footage has been shot with a recognized lens? (As is possible with still photos.)

Or could you at least manually tell your video software about the lens used and then have it correct distortions and other problems? (As is also possible with still photos.)

Thanks!