You need a A2DP bluetooth stereo headphone.

You may need to google A2DP to find out more info about this profile.

For question 1, Yes. As long as they support A2DP profile.

For question 2, I have no idea.

For question 3, currently the sound quality of BT stereo headphone is just so so. IMO, it's a little bit worse than normal mp3+3.5mm headphone.

BTW, personally I use BT headphone because of its following convenience:
1. Most of BT headphone supports AVRCP profile, so you can forward/rewind music tracks easily. This is a big plus for me.
2. In case there's an incoming call, a warning sound will be sent. You can switch to phone by 1 click. So you wont miss a call when listening music.