Speakers setup help

I currently have 5.1 speakers hooked up to my old yamaha reciever (AV-90 PY). Because my TV only has one S-Video port, and my reciever has none, and I do not have a switch box thing, I have to switch the the cables when I want to use the DVD player/PS2.

I have the PS2 hooked up to the S-Video port with the audio cables hooked up to the TV as well. I have the audio-out of the TV hooked up to the reciever.

From what I understand, PS2 games are only 2.1 so only my 2 front speakers, center and subwoofer will have sound correct? Would I need to hook up a Optical out thing from the back of the PS2 to my reciever if I want 5.1 audio in games(if the game has 5.1 audio)?

Playing a movie with DD 5.1 on the PS2 will utilize all 5 speakers correct?

Is there a better setup than this for me with what I have now or is this the only way to connect my components with what I have?

Yes.