Of course, the sun is moving. Imagine you are twirling a poi ball around your head. Now walk around the block, continuing to twirl that ball around your head. You are the sun; the ball is the earth. Relative to the balls motion, you are the still point in the center of it's orbit around you. Relative to the block you are walking around, that whole 'system' (you, the ball) is moving. And of course that block is moving... It's just a matter of the frame of reference in which you want to describe it.

Two cars are moving at the same speed down the highway. Relative to one another, they are not moving. Relative to the highway, both are moving, at the same speed. Now one driver decides to pass the other car. Now she is moving relative to the other car, easily passing it. Relative to the highway she accelerated to pass the other car. Again, its depends on which frame of reference you describe what is happening in.

But all, ultimately, is in motion, and changing. Is there, ultimately, any stillness then? Anything that remains the same? How do we recognize movement or change, if there is not stillness or something unchanging, to contrast it with? Is there, in the end, one absolute frame of reference? Physicists are still looking for one, the Unified Field. Most religions, of course, with the possible exception of Buddhism, posit an absolute frame of reference -- God or the Ultimate Ground of Being. Some Buddhist teachings on the other hand argue that there is no absolute frame of reference, and we've got to just deal with it. We've got to learn to be ok with that fact, and when we do, we become free to swim in the void.. But then, isn't the void, sunyata, itself a frame of reference? ;)

Isn't the Universe just the strangest thing you've ever seen? ;)

The second question is easier. Anywhere the sun casts a shadow, it will be opposite its apparent position... but now, one may ask, what at the poles? If the stick is at the North Pole, for example, than anywhere the shadow points it will be south. ;)