Well, some characters might be a bit critical. For example, if the fanfiction takes their personalities in a very different direction than what they are in the original Mob Psycho 100. They could be like, 'That's not really how I would act!' But on the other hand, some might be flattered by the attention and the new storylines created around them. It also depends on the nature of the fanfiction. If it's a heart - warming story, they might enjoy it more than a really dark and twisted version of their story.
Hard to say. Maybe it will if there's enough demand and the story has more to tell. But sometimes, even popular mangas come to an end. We'll just have to wait and see.
Mob Psycho manga has indeed finished. It wrapped up with a satisfying conclusion for fans. The author completed the narrative and tied up all the loose ends.