1) After Khal Drogo is killed you can find x Dothraki characters , meanwhile there is the plot card 'Burning Bridges ' in play. Could Khal Drogo still use his response as an in play action ?
No. Burning Bridges says "Players cannot trigger abilities on character, location, and attachment cards in play." The Khal's Response is an ability on a character that is in play (though moribund). So the plot directly stops the player from using the ability.
2) How do you define a 'triggered ability compared to a triggered effect ?
Straight from the FAQ: A triggered effect is any card effect that only happens because the players chooses for it to happen. So anything that starts with a bold timing word like "Any Phase," "Marshaling," or "Response" that only initiates because a players initiates it is a card effect. A triggered ability is any triggered effect that is initiated when the card is in play.