Questions about D-Link Dcs-933l

Theoretically, yes. The power supply unit says 5V, 1A. A mobile power bank with the corresponding key figures should be sufficient. The runtime would depend on the capacity.

The app and the camera itself do not have a recording memory, to make recordings you need a NAS or another storage option.

If you integrate it into a NAS (network storage), then yes. Then the recordings are saved ;-). It must be connected to a storage device that is always running. If your PC is always running, for example, it might also work from the D-Link software....