when you first create a shape it asked you what you want to input for creating different variation of a shape, but one you click away those setting are gone forever. Is it possible to insert key frames into those initial settings?
Not as keyframes, but you can create presets when you add a shape, by pressing the + sign right next to the operator presets.
By creating a preset you can recall custom settings.
Note that once you modify an object in any way there is no way to go back and re-edit the parameters of the created object.
If you want to create an animation by modifying the shape look into using shapekeys