Does the i-XLR supply phantom power?

No, the i-XLR supplies plug-in power so that in addition to dynamic and self-powered microphones when paired with the appropriate adapter, it can be compatible with the majority of lavalier and headset style microphones.

Is ‘live monitoring’ always on?

The i-XLR’s headphone output provides zero latency analogue monitoring which is a direct feed from the microphone you have plugged in. This is not affected by the analogue to digital conversion and will always be on while the i-XLR is powered.

Will I notice any difference in battery life when compared to not having an i-XLR connected?

The i-XLR does require power from the device to operate and will have an effect on its battery life. Though not significant, this should still be taken into account.