What will happen if I leave my toe fracture alone, will it heal on its own?

Usually. As long as the toe is in good alignment and it feels like it is improving, then it should heal. Stay in a stiff shoe and limit activity to tolerance. See your podiatrist is concerns.
Yes. If the fracture is not displaced it will heal. Stabilizing the digit by taping it to the neighboring one helps.
May or may not. If left untreated it may not heal as good as you would like.