I assume the 300 unit is as any other land unit, so it must stop in a theater if the condition to exit is not fulfilled.
Assuming that, I also assume that its value as stratego token is not taken into consideration for the battle when it stops in a Theater different from the Expedition Theater. But, is that movement still "free" (i.e. does not count to the total number of movements calculated from the initially committed stratego tokens), even when the unit has not stopped at the Expedition Theater? I feel answer is yes, but it would be good someone confirms that...Thanks!
Yes, it moves like a Spartan cube
Yes, if stopped short of military expedition location, it does not count. However if later on a battle occurs at its location the Strategos does count.
Yes, it does not count toward committed Strategos.