I'm playing Two-Headed Giant. I have Ajani's Pridemate, which has "Whenever you gain life...". My teammate plays a card, that makes him gain life. As we share our life total, my life is also updated. Do I get to activate Pridemate's ability, when my teammate plays the card?
No, the Pridemate's ability doesn't trigger when your teammate gains life, because while your shared life total goes up it is not you gaining life.
How does damage, loss of life, and gaining life work with the single life total for the team?
Damage, loss of life, and gaining life happens to each player individually. The result is applied to the team’s shared life total.