Very good questions. I wish more folks would consider them.
Gravity is maximum at the earths surface. Surprise ?
All the earth's mass in one side of your body.
Pendulum clocks run slower at altitude or depth.
Vibrating mass clocks (accelerometer type ) run faster at altidude or
depth.
Masslesses clocks are expected to be gravity and motion insensitive.
http://tf.nist.gov/timefreq/cesium/parcs.htm
http://bigben.stanford.edu/sumo/status.htm
http://bigben.stanford.edu/sumo/
As for time...
It waits for no man, only women. ;-)
Sue...