Fine, Betty IS a big reason Jughead stayed in Riverdale in season one(even if he tried to abandon her in the same episode that line came from) but not in the Christmas episode.

During the Christmas episode he clearly had no intention of going to Toledo from the start, check his reaction, he was mad at Gladys and FP at that point(hell he's still mad now) so typewriter or no typewriter he probably wouldn't have gone to Toledo.

And Jellybean has no idea who Alice is, let alone that FP is sleeping with her and doubt FP or Gladys or Bughead will ever mention it to her given that she's a kid.

As for the southside/northside stuff? JB's a kid, I doubt she really knew what was going on(hell Gladys doesn't even tell her things now) with that, given that she probably went to school on the northside with Jughead who was completely clueless about his own neighborhood before the serpents came along.