My laptop has a Beats by Dre logo for some reason, I have no idea why because the sound quality is no better than any other laptop I have used with bog-standard speakers.
"Beats capable", probably. Means about as much as "Vista ready".
I really hope not, it's a pair of headphones. It's not like you're plugging in a new type of RAM.
Beats licensed their name to bunch of computer manufacturers and included some kind of software equalizer presets that would make the sound more 'Beats-like'. As far as I can tell Beats had nothing to do with the actual audio hardware.