These are fairly basic calculus problems- dust off the ol' textbook.
Generally, you can just integrate volume along the vertical axis, and the integrals will be in the CRC Math Handbook or other similar references. Break the shape into cylindrical, spherical, torospherical segments as required.
For surface area, divide the area into circular strips of width (Rda), where R is the radius normal to the surface, and da is the angle.