noname, no offense, but pretty much everything you said is wrong.
Not correct.
The gravitational field of a rotating sphere is identical to that of a static sphere.
If you jump, you’re already moving at the speed of the rotation of the earth’s surface, so the trajectory of the jump will be a parabolica, added to which is the minimal effect of the gravity of the earth. But you’ll effectively be travelling at the same horizontal speed as the earth, and so land in the ‘same’ place.
errr I mean a parabola
True for the Newtonian model of gravity, but IIRC General Relativity introduces the concept of Frame Dragging around a rotating body. Granted, the effect from the Earth is very small…
On the ball in the space station… How noticeable would the degree of change on the ball be if you threw it against the rotation?
'Bout the same with the rotation. Here is a thread from last June on the subject, with graphics, from over at the Bad Astronomy bulletin board.
Wow, thank you all so much for the really great answers. I tried to explain this to my friend that originally asked the question, but he said he needed pictures. 
However, a couple other friends reallly enjoyed hearing about this. Thanks again to all of you!