I don't think dice rolls should be involved with scenario #2 - I don't feel there should be ANY dice roll that would cause a mother of two to sacrifice a child UNLESS she's already a believing cultist. That's basic human nature - it shouldn't be a 'cool sploit' that players can abuse because they've maxed their social stats and skills. Serious roleplaying should affect this scenario, and magical effects where you absolutely puppetmaster a person should also work - but not a situation where you can just dice for it IMO
I agree that words alone couldn't make someone offer up their child, but I don't think it should be completely impossible. Imagine a trolley problem scenario. If the demon wants a child offering, I think a
very skilled orator could make the argument: "It's terrible that little Timmy has to die, but if we don't sacrifice anyone then the demon is going to come up here and kill all of us."
The trope of a monster demanding one human sacrifice a month is a classic of myth and fantasy for a reason.
I would not draw the same conclusions than you. I don't think you can get anyone to act against their principles, it is just that a lot of people really do not have principles or lie about what their true principles are. Then again, in a RPG we might not have pre-established how principled every NPC is so one might just let the dice results determine that.
Im not sure if this is true. People do change, and social pressure often contributes to that. Even the most principled people develop and evolve their ideology. I agree that a ttrpg's rules probably shouldn't suppiet talking a paladin into murdering a bunch of orphans though.
This doesn't really matter either way because, like you said, most people don't have defined principles that they consciously thought of. It might be interesting if some NPCs had special resistances/weaknesses to specific arguments defined in their stat block in the same way that a troll's weakness to fire is.
When the fiction invites no conflict or no meaningful result for failure then no roll is required, IMO.
When the fiction doesn't invite a purpose for a roll.
i.e. you cannot convince everyone, no matter how much your +x on the die roll is.
I think this is true, but I don't think it's sufficient. I mean, what you say is true of pretty much all dice rolls. As an analogy, a game with a section on jumping would want to define a distance you can jump without a roll, a distance you can jump if you roll well, and a distance you can never jump. Other liter systems might not want that level of depth, but if OP is starting a thread on the topic, that level of depth is probably important to this game.
I don't think a single rule-of-thumb can cover every case, but I can come up with two that together seem to do a pretty good job. If your character is trying to exchange goods/services/favors with an NPC, I think they should roll if they offer the NPC something roughly equivalent to what they request.
You can't just talk the King into giving up his throne, but you could at least attempt to convince a struggling minor lord to give you his territory in exchange for providing him with a nice castle, and guarantee him a long life of comfort and leisure. Even that King
might be willing to consider giving it all up if you offer to save his life from the imminent invasion that would surely destroy the kingdom.
IF your character is trying to convince someone to change their ways, then you should roll if you have a good argument that resonates with that NPC. When Gandalf tries to convince King Theoden to ride to the defense of Gondor, he didn't offer up a service of equivalent value, he appealed to Theoden's insecurities. He offered a way to atone for falling for Saruman's lies, a way to leave behind a positive legacy, and he appealed to Theoden's good nature and concern for his fellow man. Such an argument would have no chance of success on Denethor.
I think there are other reasons to roll for social interactions (lying, convincing someone of the truth, impersonating someone else, trying to establish/improve your reputation, etc), but those seem like they would fall outside of a negotiation system.