A:AnswerYes, and it comes with an HDMI to mini HDMI cable to connect it. You will still need to plug in to USB as a power source with the cable that comes with it (either in the laptop or with one of those cell phone chargers either USB-C Power Delivery or regular USB cell phone chargers).
A:AnswerYes, as long as you use the both the USB TYPE C to HDMI cable and the USB TYPE C to USB TYPE A. It works like a dream. I use it to play on my PS4 all the time.
A:AnswerThe power supply depends on the device that you plug the monitor to. For example, for a PS4 (any gaming console) you need two cables: one (USB TYPE C to HDMI) from the monitor to the console and one (USB TYPE C to USB TYPE A) to a power supply (wall outlet or gaming console). Depending on the laptop it could take only a USB TYPE C to USB TYPE C cord or both TYPE C to TYPE C and TYPE C to HDMI cord.