I believe you take a minimum of 3 cards to satisfy the morale. So only 3 of the players will receive a new card for this mission.
Exactly. Always add 3 (or 4 if that hard knock is out) each round if you haven't already won or lost. After dealing those 3 (and it means 1 player may have to withdraw on their first turn), you need to play all 5 in hand to the table to win, or you'll get another 3 on the trial pile.