Yes, the players decide which goal to pursue {roll against} and can concede points on other goals as a means to gain on the selected one.
My intent with this system was to put choices in the hands of the players, and have those choices shape the adventure path. They told Lord Shaladel who took the Torch as part of the deal regarding the freedom of Gates Pass, so now if they try to recover the Torch they will have competition....
But Gate's pass won't become a vassal state to the Shahalestian Empire.
No, I didn't specify a skill because that depends on the players approach. Mechanically it is the same DC, but use of bluff or intimidate might backfire... or possibly be advantageous. PCs could use Insight to see what the best approach would be.
Technically you can use pretty much any other skill as well, as long as the roleplaying pitch supports it. Lord Shaladel is enamored with history, so a knowledge history could allow you to refer to similar times in the past that went the way you prefer... gaining successes.
In negotiations with a stereotypical barbarian, using intimidate is what he expects and he might start to dislike the PCs for 'talking sweet'. This would reflect in him pushing to close the negotiation early or possibly even shift attitude down a notch to neutral {if friendly} or hostile {if neutral}