Does Soul Link give life twice in combat and fighting?
Yes, you are correct. When damage is dealt, 2 separate triggered abilities trigger. You will choose the order in which to put them on the stack, and then each one will resolve.

An example: Your Soul Link is enchanting a 3/3 creature, which is blocking a 1/1 attacker. When damage is dealt, your creature will deal 3 damage, and be dealt 1 damage. 2 abilities will trigger: "gain 3 life" and "gain 1 life". You will put them both on the stack, and get a total of 4 life.