1. For the purposes of the overrun combat maneuver, does a 5 foot step count for the movement prerequisite for this maneuver?
Can I 5' into, or over to, an opponent and try to overrun? Or will I have to make an actual move, like 10 or more feet?
2. Will the improved overrun feat allow me to move into, and make an overrun attempt on, a creature that has reach and not trigger an AoO?
1) Two creatures cannot occupy the same space.
Overrun involves moving though an opponent's square, not into(that'll be bullrushing since you force it out of his square).
And then you're moving at least 10' so you're not 5-foot stepping.
Makes sense?
2) With Improved Overrun you do not provoke an attack of opportunity when performing an overrun combat maneuver.
You still provoke for exiting a threatened square while doing so.