The bluetooth headset is connected to the audio chain of the computer and its operating system, not to a specific piece of software like Skype. In other words, a bluetooth headset is no different from any other headphone with a built-in microphone, as far as Skype is concerned. So of course any bluetooth headset will work with Skype, provided your computer has Bluetooth.

Regarding your question about being near the computer: Bluetooth is very short range. You *have* to be near the computer to maintain the bluetooth connection. It depends on the device, but, once you start going farther away than, say, within the same room, you start losing connection. I've got problems keeping the wireless bluetooth keyboard on my Mac Mini working, when I'm on the couch and the Mini is beside the TV set.