You can guaranteed a successful down attack if properly timed (think something like Spirit cancel dash space).
SSSA gives more height than SSA. Think of it as the difference between the AS and AAS melee launchers.
AA dash AS is an inescapable alternative to AAAS.
The final hit of AAAAS knocks the opponent far away in air combos and can be used to do a Tears combo without Spirit or Shout.
S can be used to cancel dashes and can be dash canceled in any direction; some people may find it more comfortable to S cancel instead of a normal dash cancel for more precise movements.
Also, I can't say I totally agree with the etiquette section. It's true that healing and hit-and-run tactics are very difficult for beginning PvPers to counter, but if your Dodge is on cooldown, it's murder for an Eir to play a close game against another class of equal skill. There's no need to abuse them if you can win without them, but serious PvPers should be aware of ways to use them effectively or you're likely to struggle at the top levels of PvP.
"It is not a disgrace to fail. Failing is one of the greatest arts in the world," however --
"Believe and act as if it is impossible to fail." ~ Charles Kettering