I was just reading he FAQ and it says in section 3.20 that paying a cost with influence is not triggering an effect. Does that mean that if my opponent plays dance with dragons I can't respond with seasick? Am I misunderstanding something?

There are instances where you can pay a cost with Influence TO trigger an effect. However, the act of kneeling influence to pay a cost is not triggering an effect by itself. Sometimes you can pay a cost with influence for purposes other than triggering effects.

For example, you can kneel influence to help pay the cost to marshal King Robb's Companions.

By doing this you are not triggering an effect by kneeling influence.

I think the FAQ's entry on that is an attempt to generalize that paying costs with influence is not something you can cancel and that you'd have to save from or cancel the effect itself that is triggered by kneeling the influence as it's cost.

And to answer your question about Dance with Dragons, yes you can respond with Seasick to cancel it. The kneeling of influence to cancel Seasick is not a triggered effect by itself.

What the FAQ entry means is that kneeling an influence-providing card to pay for an effect with an influence cost cannot be separately canceled (and thus letting you argue that the cost wasn't paid, so the effect with an influence cost was not triggered).

For example, say that I kneel Missandei to pay for Dance With Dragons. You are free to use Seasick against the event I triggered. But you are not able to use the Lanni-Iron Throne to say Missandei did not actually produce the influence needed to pay the cost of the event.

When kneeling influence to pay or ambush, I take it that the kneeling is one action without intererence

By that I mean that if I had to kneel two locations to "pay" 4 influence, someone cannot trigger a response to me kneeling the first location

They might be able to do that in the case of King Rob's Companion as that is the equivalent of paying the cost twice ~ but maybe not !!! - you are kneeling to pay, not reduce the cost

For Ambush are am pretty sure that the influence is knelt as a single action?

I'm particularly thinking of an opponent with Hellholt Docks

Response: After an opponent kneels a location, kneel Hellholt Docks to choose and kneel a location.

Yes, all influence is knelt at one time to pay the cost. You might have a few other confusions here, so let me clarify

1. Initiate an action (Pay All Costs, be it gold or influence or kneeling characters, all at once)
2. Save Cancel opportunity (In this case, can't cancel Ambush as it cannot be cancelled)

3. Effect Resolves (Character comes into play)

4. Response Opportunity (This is where Hellholt docks could be triggered to kneel a location, since your opponent did kneel a location).

It's probably important to note that kneeling the influence (which is indeed knelt all at once) is not an action in and of itself - any more than paying gold is an action in and of itself. It is paying the cost of an action, which must then resolve fully before any Responses to any part of it (cost or effect) can be played.

This is different from using things like the Seas, the Streets, or the Fiefdoms to reduce the cost to play something. It's a common "shortcut" in play to, for example, kneel three Fiefdoms and pay 2 gold all at the same time when playing a 5-cost character. This is technically incorrect because the you are not kneeling the Fiefdoms to actually pay the cost, but to lower the cost you eventually pay.

So kneeling 3 Fiefdoms to trigger their own cost-reducing abilities and playing a 5-cost character is a total of 4 actions - while kneeling 3 Fiefdoms to pay the influence cost to Ambush in a 3-cost character is just 1 action.

Thanks for the confirmations Ktom & Istaril