Whether they have any extant function or not, they have lost their former function and in that sense they do fit the definition of vestigiality. Vestigial structures are often called vestigial organs, although many of them are not actually organs.
There are quite a few birds famous for doing ritualized mating dances, so I would only list 5: The Red Capped Manakin, The Black-footed albatross, The Western and Clark's grebe, The Superb bird of Paradise, & The Victoria's riflebird.
Confidence votes 366. Depending on the species, hummingbirds can flap their wings anywhere from 40-80 times in one second, with the fastest being 90. During courtship, wing speed will increase further--even up to 200 times per second. A Ruby-throated Hummingbird, hovering in open space, has a wingbeat rate of about 50-52 times per second.