Player 1 plays the "reinforcement card". Can player 2 use the "counterattack" card on his turn to also get reinforcments? My almost certain assumption is yes. The one thing that makes me wonder is is that the card says counter-ATTACK. making me think that it's really only to be used against cards where the opponent is actively attacking.
Yes. The titles of cards are for identification and flavor only. They do not create any rules themselves.
The counter attack card, in essence, allows you to play a duplicate card of what was just played.