“After moving a Ram, move up to 2 troops from this region to a single adjacent one. You may spend 1 Corra to deal 1 damage to each of these troops.”
If a Ram moves twice, does its ability trigger twice? (yes)
If a Ram moves two times, if for example you move it with a Maneuver action and then use the All-Seeing Double result to move it again, its ability triggers both times it moves.
Can you use the Ram's ability to move your own troops? (yes)
Yes, you can move your own troops with the Ram ability. However, you cannot damage your own troops, so if you spend the 1 Corra to deal damage to the moved troops, that damage would not be dealt to any Runen troops that were moved.