Well, the DM doesn't decide (in that example) if the NPC helps or not, just the degree to which the NPC will help.
Or the DM wants to allow the roll to dictate the degree of assistance (which I believe is your concept).
Or the DM could also decide (due to role-playing or the desire to forward the adventure), that the NPC will help and no roll is needed.
Or the DM might decide the NPC won't help (because the adventure requires the PCs look for an alternative or just wants them to "walk").
In 5E, the DM calls for the roll when the result is in doubt. In the 3rd and 4th, there is no doubt--the NPC will help or won't as the DM dictates. The 1st and 2nd leaves the outcome in doubt, so asks the player to roll. How the DM deals with the success or failure is up to them, of course.
Well, that is the thread title, sure, but he goes on in the OP to ask a bunch of questions about it.
Anyway, for the most part, social challenges in 5E should be resolved via role-playing as much as possible, not roll-playing, IMO. It is the only challenge we can easily resolve without dice rolling. Combat can't really be "acted out", nor can exploration challenges. So, we have rules and resort to rolls to resolve them.
Can you hit the creature attacking you? Make an attack roll.
Can your PC swim the river? Roll a Strength (Athletics) check.
Can you convince the guard to let you into the prison? Role-play it or make a Charisma (Persuasion, Deception, or Intimidation) check.
We know combat requires multiple rolls to resolve due to how it is designed in 5E and the stakes involved.
Can swimming a raging river require multiple rolls to resolve as well? Certainly, and depending on factors, a DM might want a single roll for success or several.
You can certainly require multiple rolls for convincing the guard, but you can also role-play it out. For a role-playing game, why would you choose to roll? Maybe they are newer players who aren't comfortable with it, but otherwise I would think encouraging this part of the game is sort of the point of it being "role-playing".