"Would you like some breakfast" isn't quite so overly wordy that I'd say it sounds unnatural, but it absolutely is not the bare minimum for idiomatic English.
"Do you want breakfast?" is perfectly grammatical, and "Want breakfast?" would be a totally normal phrasing, even if some might argue that eliding the subject isn't technically correct.
No it doesn't. I don't ask my colleague "Would you care to go to the bar and drink a beer after work?" I say "Grab a beer later?" As does every other normal person I know. "Get lunch?" Etc.