Standard 3G-SDI converters support up to 1080p at 60fps. For 4K monitoring, you would specifically need a 12G-SDI to HDMI 2.0 model.
Yes, it requires a 5V power source, usually provided via a USB cable connected to the camera's USB port, a V-mount battery, or a wall adapter.
Yes, this is the primary use case. It converts the professional SDI output of your camera into an HDMI signal that any standard TV can display.