It should be face up, yes. Catching simple grammar mistakes isn't my strongest suit. And if a unit takes damage during the turn, that damage stays on the unit until the end of the turn, where the unit will heal to full hp. I'll reword that as well.

haven't played the game yet but looking to give it a try, just reading through the rulebook ya got here and i see the "When you play a card, put it face in in front of you." at the first line of playing cards section, i'm assuming you mean play it face up?

then i'm at the battle phase section "Any unit with damage on it loses that damage, and the turn is over." does that mean like they have damage on it if i can't do anything to remove the damage it loses hp equal to the damage that's on it? or that if it's not kill it loses the damage on it and it goes back to full hp?