1. The steam deck usb-c port (also the charging port) does support video and audio output. Please make sure that your monitor has speaker, connect your steam deck to the monitor with a USB-C to HDMI cable and everything should be fine.
2. It is uncommon to see that a monitor uses usb-c as audio/video input, most likely you could find one in a portable monitor. Before you try to connect them with a USB-C to USB-C cable, please make sure that specific USB-C port (monitor) supports HDMI interface.
Note: I would suggest you buying a dock station (that supports HDMI interfaces) for your steam deck in order to charge your device while connecting to an external display.