No, the 3G model supports resolutions up to 1080p at 60fps. For 4K workflows, you would require the 12G-SDI version of the converter.
It is powered via a USB-C port. You can plug it into a wall outlet using a 5V adapter, or power it directly from a camera's USB port or a power bank.
Yes, this is the primary use case. It converts the Sony's HDMI output to SDI, which is the standard input for professional switchers like the ATEM Television Studio.