Yes on the first part of the question: HDMI from each device to the AVR and an HDMI from the AVR to the TV will provide audio from the sound system speakers. You may need to disable the HDMI audio output from the AVR to the TV in order to get surround sound. Sometimes the HDMI handshake with the TV tells the receiver to produce stereo instead of 5.1 because TVs are only 2 channel devices. Check the sound system manual for information about the HDMI audio output.
If the TV and the AVR are both HDMI 1.4 and include support for ARC (Audio Return Channel), then you can back feed audio from the TV apps to the sound system over the same HDMI cable. The manuals should explain how to setup ARC. Otherwise, you can use an optical cable between the TV and the sound system.
btw, there's no need for an HDMI cable with ethernet. No devices support ethernet over HDMI at this time. Regular High Speed cables will work just fine.