I think the last I had read was that there are now approximately 160 "extra-solar" planets believed/presumed to exist. We can't actually see these planets as such, but we can detect the effect they have on the brightness of their parent star as the planet passes between our point of view and it's parent star, and when this happens on a regular and predictable basis they tag it as another extra solar planet.
As for relativity and rotating objects I don't see any problem - travel in a given direction (be it a straight line or curved path) is due to a separate set of forces to the actual rotation of the said object.
Any 17 year old guy with a rear wheel drive car and a wet grassy paddock can tell you that direction of travel and the direction you're actually facing at any instant frequently has nothing to do with each other at all!
Cheers!