I don't really understand where you are going with this question. Why do you need to calculate focal length? For most, what is marked on the lens is sufficient.

Covering power: seems to me people look it up on the web, in lens brochures, or try the lens. Some, maybe, can remember all the lens types and coverage.

Depth of focus is marked on smaller format lenses. There are DOF calculators and there are the same on the web that are Excel based. Here is the Rodenstock model:


The formulas are in most photo texts.

There are some freeware ray tracing programs on the web. Mostly used by and designed for the telescope folks.