I always thought that phalang - is just the army boost - so the composition of the army means nothing.
But maybe I'm wrong - if my army is solo horses - and enemy army is also solo horses - will the phalang do any matter?

If I have many horses and small amount of rangers - and the enemy small amount of infantry and many horses - should I use ranger or cavalry phalang?

a phalanx is a formation. each phalanx has a different order of troops.
infantry phalanx has the order: infantry-calvery-range.
calvery phalanx has the order: calvery- range-infantry.
ranged phalanx has the order: range-infantry-calvery.

it decides which troops you want up front. if you do a single type attack like calvery, the phalanx doesn't matter. but when you have 2 troops types like calvery and range, it can decide which troops go upfront and thus get attacked.