Is it possible to connect a Bluetooth stereo device like headphones or earbuds to both a mobile phone and a computer at the same time, so that I can listen to music from my computer, but also make/receive a phone call from the mobile phone?
You would want to search for bluetooth headset with "multipoint" technology. However, the downside of this kind of headset is that the quality will decrease along with the increasing number of devices connected to it.
The better solution would be to put your music in your mobile phone and connect the headset to only one device. You'll get better sound quality, plus the feature of pausing the music whenever there's an incoming call.
You have to make sure that all your devices are capable of connecting to multiple devices simultaneously.
For example, one of my mobile phones, to send a picture, I had to manually transfer each file on the phone separately, I couldn't just open the contents of my phone on my computer and copy and paste.
Also, blue tooth can be relatively slow, so you will have to be streaming your music at a low bit rate, and if you are streaming to multiple devices, even slower.
I have a Bluetooth headset and stream high quality audio just fine, I think BlueTooth can support audio streaming without any issues. http://en.wikipedia.org/wiki/Bluetooth
I should rephrase what I said: sending files via bluetooth can be relatively slow compared to other methods.
But yeah, Aibek, you are right.
Yes, I believe it is possible. Most Bluetooth devices can support multiple devices at the same time. You simply have to follow the directions for syncing that came with your headset/device and sync it to each component one at a time.
I would start by syncing it to my phone and testing it to see if it works. Then, sync it to the computer and test everything and you should be all set.