1. ofc, take Xenophon's account of Cunaxa, flutes gave the rhythm, and the "awareness" of nearby companions made everyone try to stick together...

2. run as fast as people with 30ish kg of gear on, who had to fight after the "run"; the Spartans went for an "advancing shieldwall", most likely they walked: their intent was to keep formation "intact"...

3. no, sometimes it was a tactical move by the commander to flank the opponent, if we take again Cunaxa placing hoplites to the left of a river would be suicidal, as they would jump into it :P