Can I use the OMNIS-DUO to mix music from a mobile device that's connected to the unit via Bluetooth?

Yes.

You can mix music from a connected Bluetooth device by inputting it to channel 1 or 2.

If DECK is selected and music is input to LOAD 1 or LOAD 2, it can be input to DECK.

Note: Music played via a Bluetooth connection will be delayed before it's output from the OMNIS-DUO (this is due to latency caused by the Bluetooth connection).