Why do TV networks air pilot episodes of a series that has already aired a first episode?
A TV pilot is a scripted and filmed “first episode” of an intended series. It is usually used to test the waters of whether or not an idea for a TV show is viable and marketable.
Why do they call it a pilot episode?
The first episode of many TV series is called "Pilot" because the episode functions as a pilot for the series, just as a "pilot" is a person who operates a "plane", in comparison, a pilot episode therefore is the "take off" episode of a TV series.
Irrespective of the result (good or bad ratings) of the pilot episode, would the network continue to air the series anyway?
Often a TV pilot will never air because no network shows interest in the project. Sometimes one network will produce a TV pilot, and another network will “pick up” the show and air it, because the original producing network is not interested after viewing the TV pilot.
If a network expresses interest in the TV pilot, they may use test audiences to see how likely the pilot is to be appreciated, before committing to producing a series. If a test audience responds favorably to the TV pilot, then the network may choose to make a series, which expands on the premise of the pilot.
By the time they actually start airing the series, wouldn't they have the complete season 1 in hand?
This depends, on the network. But once a pilot has been approved then a certain number of episodes will be "green-lighted" or ordered by a network. Some TV series has complete season episodes written (but not filmed) by the time the pilot episode is aired.