Quick question how did you make the star, did you use the pen tool set to shape, if so you can use the direct selection tool to pull and drag the anchor points, you can also move the handles around and adjust as needed
Yes you can edit shapes drawn with the shape tool, here's a butterfly shape from the standard shape tool menu, as you can see you can select the anchor points and control handles, just make sure you have the direct selection tool selected after drawing the shape
Also make sure not to rasterize the shape layer otherwise it won't work