#triggered ability

[magicjudge]

I feel bad about this, but I need to know what should've happened. My opponent ultimated sorin, and so at the beginning of my upkeep I had to sacrifice a creature. The first few turns after he got the emblem, I followed the rule. But then, I noticed he forgot about the emblem, so I played a tasigur and didn't sacrifice it like I should've. 4-5 turns later, I'd beat him to death with my tasigur and won. If he noticed it later in or after the game what would've happened competitive REL wise?

You’re never required to point out your opponent’s triggers at any level of tournament. While it would be the nice thing to point out the triggers, you’re absolutely allowed to leave it up to that player to remember triggers from sources they control.

[magicjudge]

If I control two permanents, on with a triggered ability and one with an activated ability, and part of the cost to the activated ability triggers the other ability (ie. a sacrifice cost) which ability resolves first? Do I choose the order?

The triggered ability will always resolve before the activated ability whose activation triggered it.

[magicjudge]

Can Vipers Kiss be used to stop Gift of Immortality from triggering?

No.

First of all, Gift of Immortality has a triggered ability, not an activated ability. And that ability is on Gift of Immortality and not the creature. Viper's Kiss doesn't do anything here.