Yes you can if you the detach the light itself from the pole. You can mount it on very tripod with a 1/4-20 screw.
I personally have it mounted with the included pole and the elgato heavy base

I would think so. It has a screw hole for the usual fitting you see on consumer cameras and the like (the 1/4-20 UNC standard). The arm it ships with is nice and sleek for a desk setup, but you're not limited to that.