For the record, we have seen a form of mind control magic in the show already. Twilight's "Want it, need it" spell. Would be a safe bet that other more sinister spells may exist.
Also, I doubt we will be getting much more backstory on Starlight, it can be inferred that after her friend (Starburst?) got his cutie mark and she developed her hatred for them, she became obsessed with finding a way to remove them, once she learned the spell, she earned her cutie mark, which is why her cutie mark depicts the magical removal of a cutie mark. She would have had to have been naturally powerful in order to use such an advanced spell.
As for her gaining access to time magic, she already spelled it out: she took the same spell twilight used before and modified it to interact with the map. As she said Starswirl already took care of the hard part, the actual time manipulation part of the spell, all she had to do was augment it with the maps magic. The map gets its magic from an extremely powerful source, the Tree of Harmony, so it wasn't even really her power that allowed her to travel so far back in time, it was the maps. This also explained why the map persisted throughout every timeline, it was connected to starlight's spell. If she had sucessfully destroyed the spell, the map would have likely vanished from the alternate timelines leaving Twilight and Spike stranded.