You don't need the TV to have s-video to record from s-video. Just send the s-video end to your capture device and the yellow cable to the TV. And yes, recording from a Wii is better because it's a sharper picture, even with the yellow cable. S-video from GameCube will show a faint checkered grid of pixels
And yes, your new videos look really good. For audio during recording, you have to choose a bit rate and frequency. I think most applications work best with 48000 MHz? For the audio problem, try cutting down the bitrate to 128 kb/s and see if you still get any desynced audio. Make sure you don't run any resource heavy programs during recording
What are you computer specs? (processor, ram, video card)