External Speakers Setup

Hi, I think I have fair idea on how to set up everything but I would like confirmation.

I just bought a HDTV (with inbuilt digital tv tuner) and a DVD Receiver which has 5.1 speakers/sound.

I would like sound via these 5.1 speakers while watching free-to-air digital tv
and also free-to-air satellite tv (international channels via satellite) intead of using the tv speakers.

The satellite box is connected to the tv with the yellow, red and white connecters which I think are called RCA Plugs. Im pretty sure the satellite is of digital signal, but since its connected with RCA plugs it's not outputing digital sound, only analog.

At the moment only when I watch a dvd the 5.1 speakers are used (obviously as the receiver plays dvds and the speakers are connected directly to the receiver).

While watching normal digital tv and satellite tv the sound comes out of the tv speakers.

By using a digital optical connection from my tv to the receiver that should produce sound when im watching normal digital tv. But what i'm concern with is with this connection will i be able to have sound from the external speakers when I turn on AV1 that has my Satellite TV connected by RCA Plugs.

My satellite box doesn't have a digital optical output, so if I connect my TV digital output to the receiver input with optical connection will i still be able to have sound for the satellite TV on AV1, even though its analog, through my external speakers or will it only produce sound for the TV speakers? (I dont mind if its 2.1 and analog sound). It would be a nuisance as im told you have to turn off your tv speakers when you connect external speakers so you dont get an echo and then have to turn them back on for my satellite TV.

Also another question is about HDMI? If I connected it from the TV to the receiver what will it do? Does it just improve the picture and sound quality when watching a DVD? I dont have an external digital settop box (for free-to-air digital tv) as mine is inbuilt in my TV do I miss out on improving the picture and sound quality of digital FTA TV? Or can I watch FTA digital tv if I press HDMI (will it pick up the channels?) on the TV and then HDMI on my receiver?

Thank you for any help
Alexio