Suppose Predator's Rapport's target has counters (for example, a few +1/+1 counters). Do the counters count when calculating the gained life? I thought power and toughness do not change after adding counters.
Yes. When a card refers to any creature's power or toughness, it always means the creature's current power or toughness, not what is printed on the card. This includes any +1/+1, -1/-1 or other counters that modify power and toughness; any equipment or enchantments attached to the creature that modify power and/or toughness, and any effects from cards such as Giant Growth, Glorious Anthem, or Bile Blight.
Note that damage on a creature does not change its toughness.
+1/+1 counters count for power and toughness. The power and toughness of a creature are modified by counters in Layer 7. You can also change the P/T with other spells, such as Giant Growth. Giant growth is also applied in Layer 7.
It's hard to explain in a few sentences, but more info about the layer system is explained in this article.