1) It represents a distant reference, sometimes called isopotential ground. A recording electrode would fall somewhere between ground and the axon diagrammed.
2) When the action potential actually arrives, sodium channels open and sodium ions flow inward. This inward flowing current constitutes a sink. Because the sink is created by a change in conductance it is dubbed active. Because positive charge flows away (and thus the exterior of the cell is relatively negative), your electrode will register a negative potential.
Whip that axon round and round!