A:Answer To connect to an AV receiver your receiver would need to have either an HDMI "ARC" or a Digital Optical connection. It depends on how old your AV receiver is. I would imagine if your receiver was purchased in the last 7 years it probably has, at minimum, a Digital Optical connection port.
As far as your Direct TV receiver, in order to get 4K resolution, you would need to connect through HDMI and the Direct TV receiver would need to support 4K. If it doesn't you need to switch the receiver through them.