Frisk goes wherever you click. Btw, when the determination sprite pops up, there's a certain way to "save your game". For the first star you encounter, press 1. For the 2nd one you encounter, press 2, and so on. If you do this out of order, like pressing 3 for 1, it might mess up. It might also mess up if you press the number before seeing the star itself.
Toby Fox owns Undertale, not me. I just made the interactive project. It's not 100% finished, but I hope you enjoy this anyway! I also plan to add more characters later on.