Ok, so I tried it out on a new save file, and it turns out when you game over on the tutorial levels you can continue FOR FREE, making lives basically pointless. That's fine I guess. They're for learning I guess. The first stage in Twisted had no timer either.
And yes, turns out the "pay to continue" option only appears during your first playthrough.
The thing is, during all of my first playthroughs of the story mode stages, I just never lost! So that's why I never saw that option.
However, that still doesn't explain why I never got that spotpass info share option...