Yes, the headphones can continue to be used in so-called 'passive mode' even if the battery is flat, but without the NoiseGard function. For details, see the operating instructions on page 39 (under 'Using the audio cable').
By cable yes. However, without NoiceCanceling and the sound adjustment via the CapTune app does not work then either.
In my experience, the battery of the phone is rather flat than that of the headphones. Incidentally, it shows you the battery level of the headphones next to the Bluetooth symbol.