Mine definitely only pairs with one device at a time over BT. Once connected it becomes invisible to other BT devices.
For that reason I use the BT connection with my computer and ANT+ connection with my Garmin for dual recording. No issues that way
Battery definitely replaced. I bought a 24 pack of the batteries and replace them when I start getting warnings.
I might see if I can get the Android app to connect if it is the only thing around, no watch, bike computer, anything else, just to see if something is getting in before the app and grabbing the only connection.