Spheres and cylinders are studied in geometry. In fact there is a geometry that just deals with spheres called spherical geometry. Imagine living on a sphere ( you almost do) compared to living on a plane. Some geometric postulates must be modified for this.
There is a geometry of living on the surface of a cylinder too.
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Yes, you can also use pi with spheres and cylinders. :D
The formula depends on what shape you're working with. Triangles, circles, parallelograms, squares, trapezoids, ellipses, hexagons, prisms, cones, spheres, cylinders, etc. all have different formulas for their areas.
They have at least one circular base.
You study.
Not sure what you mean by "math form of pi". Pi is the ratio of the circumference of a circle to its diameter. The same relation applies to spheres. Since spheres and circles existed before the first human being, the relationship also existed. Therefore, no human could have created pi.