Hi Felwys,
I'm not an expert at skies, but to make the texture look better, try using a skybox instead of a skysphere. You can use the MAKE OBJECT BOX, or MAKE OBJECT CUBE, it doesn't really matter.
The reason you can't see the sphere when it gets bigger is because it's out of the camera's range. To solve this problem just use
SET CAMERA RANGE <big_range_number>
The default range is 5000.
To make the sun go from morning, noon, evening, night, and all that you can use an animation. I'm not quite sure about loading an avi or gif directly onto the object, but you could also take it apart and have an animation algorithm.
I don't know about the sun-in-the-lens effect, but no doubt one of the smarter guys around here will come and help you out.
Crazy Donuts
Juvenile Industries
Current Project: KillZone(FPS)
Soon to come:An rts, and a snowball fight game