Yes, it can be powered by Sony NP-F series batteries (like the NP-F970) or a 5V/2A USB power bank, though output is limited to 10W compared to 30W on AC power.
The SA-P is a lens-based accessory that fits the S30, allowing you to project sharp shapes, use gobos for textures, or use an iris for precise circular spots.
No, the Godox S30 is a daylight-balanced light fixed at 5600K. To change the color, you must use color gels with the included barndoors or projection attachment.