Normally I would elaborate on my points, but I can't really be bothered right now so i'll be short and to the point.

Alexander The Great had alot to work with.

He had the near total loyalty of the macedonian people (after he removed his chief competitors), he had the army that was created by Phillip the II (or atleast, redesigned by him). And he was facing a vastly inferior (in both training, and equipment, not in numbers) force throughout his entire campaign in Persia.
Not really. He used practically the same army throughout his campaign, just adding more and more local auxiliaries to it to make up for Macedonian losses throughout his advance. The Persians as well had the Immortals which were the elite core of the army as well as heavily armoured mercenaries such as the Greeks they employed which would fight in their traditional phalanx.

Not to mention, many times, he chose the battle-ground to fight on (ground that favored his troops, more often then not).
Did he? So at Granicus, Issus and at the Hydaspes it was part of his plan to have to advance across a river while the enemy was camped on the other side? You certainly can't say the same with Gaugamela either, since Darius precisely chose to fight there to try and make full advantage of his resources.