so #1 isn't possible as written. Maybe do it over open ocean and build a platform to secure the cable once it reaches that level... or right to the bedrock at the bottom of the sea.
You might want to build the station, or the base for the station, at a lower altitude and then drop the "rope" and once it is near where you want it you fire rockets to move the station into a higher/slower orbit that is geostationary.
That spool of cable that is dropped to earth would need to be able to be anchored to the sea floor, at least temporarily. I don't know why you think a plane would be involved.
You might not need to drop the finished cable from orbit. Maybe just a "guide rope" could be dropped. Then you attach the cable along with a smaller version of the "elevator" and use it to lift the cable along the guide rope to the station.
Anyone who has read the last of Clark's Space Odyssey series is familiar with this concept. It may even happen someday but I doubt it will be in my lifetime.
http://en.wikipedia.org/wiki/Geostationary_orbit
^snip^
A geostationary orbit, or Geostationary Earth Orbit (GEO), is a circular orbit 35,786 km (22,236 mi) above the Earth's equator and following the direction of the Earth's rotation. An object in such an orbit has an orbital period equal to the Earth's rotational period (one sidereal day), and thus appears motionless, at a fixed position in the sky, to ground observers.
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