It has no rechargeable battery, so it is powered via a fixed power cable. Its use outdoors is probably limited, as it is almost certainly not waterproof.
With the Key Light Air, there is "only" the supplied table stand - i.e. no possibility to attach it to the table or its edge. In my opinion, this is only possible in combination with the optionally available "Elgato Multi Mount (bracket)", which offers a table attachment similar to Key Light. According to Elgato specs, the Key Light Air is also compatible with the Multi Mount.