USB-C port is only for charging (you see the icon above the USB-C port is not a USB icon).
Power from USB-C is not required to use the HDMI port or the USB-A port. You might want to connect power if you're going to be doing something for a long time such as watching movies.
USB-A can connect any USB device. Anything that uses a standard USB device class driver should work. Audio, mass storage, video?