Yes, this display is compatible with a MacBook Air. To connect it, you'll need an adapter or adapter cable that converts the MacBook Air's Thunderbolt port to the display's DisplayPort or HDMI. For example, a USB-C to DisplayPort cable will work perfectly. The display has DisplayPort (2x) and HDMI (1x) ports, as well as a USB-C port, making it easy to connect to a recent MacBook Air equipped with Thunderbolt/USB-C.
Yes, the monitor has an integrated docking station in the form of a USB hub. However, there is no RJ45 connection for a network connection directly on the monitor. However, it is possible to connect to a notebook via USB-C and use Power Delivery. If you need a network connection, you could use a USB Ethernet adapter connected to the monitor's USB port.