If you have any insight on this, it would also be nice to know whether there's a big latency between connections.
The Bluetooth protocol specifies that connections are point-to-point (hence the term "pairing"), but different profiles can be used concurrently with different stations. Each profile only supports one connection at a time. You can have a stereo headset connection with your car and a data connection with your laptop at the same time, but not multiple data connections.
Correction: you are correct that I was incorrect. Quoting from this link:
Bluetooth-enabled devices are organized in groups called piconets. A piconet consists of a master and up to seven active slaves