I would question def #2. The usual term for a witch's vehicle is a broomstick, for whatever reason. Perhaps simple "broom" is sometimes used by I can't recall ever hearing it, and I can't recall "broomstick" being used outside the context of witches. I have a hunch the definition might be translationese from looking in a dictionary.
PS the "stick" part of "broomstick" has confused me since I was a kid... Can anyone shed some light?
The "broom" is the brush at the end (after the plant it is made from ; the name is related to bramble), and the "stick" is what you hold it with (or ride on, depending on your occupation), but it seems pretty straightforwardly "stick"—perhaps the compound is meant to disambiguate the broom from the broom plant.
As for use, Harry Potter, to take a recent example, uses both broom and broomstick interchangeably, though I don't deny the word "broomstick" by itself seems more iconic of the flying experience. —Muke Tever 02:19, 16 Jun 2004 (UTC)
I haven't ever heard of someone "brooming the kitchen" and would only wonder what language they mistranslated it from, if I heard it. The onomatopoetic sense seems plausible, but would be an interjection, not a noun, right? The "travel" sense seems pretty inexplicable. --Connel MacKenzie 18:25, 14 June 2007 (UTC)
I've never heard it, but I suspect the origin of the "travel" sense is from witches travelling (flying) on broomsticks. At a guess it might some Harry Potter fan fiction thing, but I've not looked. Thryduulf 19:13, 14 June 2007 (UTC)
I think the "travel" sense, if it does really exist, is likely an extension of the "vroom" sense. At any rate, I've now cited the first verb sense, but as I'd never heard it before this RFV, I'm not sure if it warrants some sort of sense label. —RuakhTALK 19:45, 14 June 2007 (UTC)
This suggests a meaning of 'brushed', by the way (but I don't suggest adding that until more evidence is found) :
1983: Margaret Walden Froehlich, Hide Crawford Quick, page 104
It occurred to Gracie as they went inside that she had never before gone in from playing in snow without having to be broomed off first.