Assuming a solid, opaque sphereworld, there won't be any sunlight on the outside. On the other hand, if you have the technology and resources to build a sphereworld (which, incidentally, practically no one would), then you can proabably find a way to get enough light and heat on the dark side.
I don't know why you'd assume there wouldn't be things on the outside, anyway.
As for the original question, a ringworld could turn to give the desired amount of centripetal force to be equivalent to gravity, although that would be part of the already absurdly enormous engineering problem.
The sphereworld ... egad. If you have the technology and resources to actually do such a thing, then I expect you probably just use whatever magic gravity-making tech you probably mastered a few thousand years earlier, to make it work. But, generally speaking, yes, if you spin to 1G at the equator, the centripetal effect would get less and less as you moved away from the equator towards the poles, where there would be no centripetal force, and yes things approaching the poles that weren't held some other way would fall towards the sun.
I haven't done the math for over ten years now, but I hypothesize that the mass of the sphere itself can't be used to compensate unless it is very uneven, because an even sphere of any mass would still have it's center of gravity in the center, where the sun is. Perhaps by using a ridiculous amount of mass increasing at the poles, actual gravity could take over at the same rate that centripetal force tapers off, resulting in an even 1G everywhere on the inside of the sphere.
Again, though, there are so many other problems of ridiculous scale in the proposed project, that if you can solve all of those, I expect you've got plenty of solutions for keeping objects from falling inwards... and probable, even more good ideas for other things to do besides build a sphere world.
Besides, your plants and animals will get really confused by having it always be 12:00 Noon according to the sun. I sure wouldn't want to live there.
PvK
[ November 24, 2003, 05:15: Message edited by: PvK ]
Re: Thoughts about sphere worlds
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