You can definitely use your BitBox02 with as many devices as you wish to, as long as they appear in the list of supported devices. The BitBox02 device password that you need to enter each time you want to use your BitBox02 stays the same on each device you use your BitBox02 with.
A BitBox02 can be paired with up to 5x devices at the same time. If you want to use it on more devices, you will have to re-pair by confirming the pairing code matches when asked for it. This behaves like a FIFO queue with 5x slots, where the oldest pairing is replaced by a new pairing when required.