Well the satellites would eventually get to be a bother, considering how many there are. If you chart all of their paths, you're bound to have tons of collisions eventually. Also, I think there's not gonna be AS many satellites, but as cheap as it'll be to launch them, people will shoot off a few. What about some sort of Huge anchor station on the planet, while the end of the elevator geosynchronously orbits earth, and you connect the supports and shaft when needed? I mean gravity would be problematic but it saves on material stress and weather problems.
Question 2, just out of curiosity, what happens when lightning hits the tower and is conducted out towards space?