hdmi vs digital optical audio

My DX-C390 CD player and HT-R390 AV receiver are connected by the RI (remote interactive) RCA cables and digital optical audio cables. The CD audio source signal comes through as analog, but I am not sure why.

The receiver and my TV (Sony, not RI compatible) are connected by HDMI: TV-HDMI out; amp-HDMI in. The TV digital optical audio-out is connected to the amp digital optical audio-in, position #2 marked TV/CD. At the same time the CD player digital optical audio output is connected to the amp's digital audio input, position #1 marked Game. The signal from the CD player is analog, indicating it is coming from the RI RCA cables.

Since there is only one TV/CD digital audio input on the amp, how do I get the amp to accept the CD player's digital output?



If the TV is off, and the CD player is connected to the Game input, will the digital signal be picked up if the amp input selector is set to Game?

Why is an optical digital audio connection required from the TV to the amp if both are already connected via HDMI? I believe the HDMI allows the TV audio to be outputed through the amp into the home theater system speakers-this works fine.

What happens if the TV HDMI-out is connected to one of the unused HDMI inputs on the amp? I am only using one for the DVD player and this works fine.

thank you