It depends
Recent receivers have multiple HDMI inputs and the intent is that you have one HDMI output per monitor (TV). This way you plug all of your sources (ATV, BluRay/DVD, Cable, etc) into your receiver and then you use the receiver to switch sources. In this case the digital audio is also carried over HDMI from the source to the receiver and you do not need a separate digital audio (coax/optical) input for each source.
BUT this is relatively recent. Older receivers had multiple other kinds of input (composite/component video/optical audio/RCA audio) so you would have different audio and video in. In this era it was not unusual to send the video direct to the monitor, not thru the receiver because the receiver may not have always been able to switch video. So you would plug in your various sources to the TV direct, video only and switch the video source using the TV input. In this case you might be using the receiver to switch audio only.
SO the answer is: it depends. If you have a modern type receiver, switch everything thru the receiver, it is simpler.
And to answer your other question about audio over HDMI vs audio over optical the answer is also "it depends". Most of the time HDMI will carry it just fine but there are some types of recent complex audio that require a certain recent HDMI implementation.
Hope that helps
