There is no rule for which net to use. It is because doubles are played on the same tournament (venue) at the same time. It is easier to just place sticks under the net for singles rather than changing the whole net.
There is no (O) abbreviation, at least not in English. Maybe you meant WO or W/O which means, that player advanced to the next round via walkover. Walkover means, that opponent has retired from the match even before it started.
128 players compete in the singles main draw of Australian Open.
104 spots are given to players with highest ATP/WTA ranking at that moment. If some of the 104 top players will not participate, next top ranked players will replace them.
16 spots are given to qualification winners (Q). Players qualify to qualification based on their ranking, like in main ...