gamecube battery life question

Battery life would be around 1 3/4 hours - 2 hours.

That screen is 16:9 so everything will be stretched.
First, I really don't recommend that battery. It has no protection circuit, which is generally a bad idea. Second, that screen, like those guys said, will stretch the image. It may not look too bad but there is no reason not to use a different, non-stretchy screen.