Convex analysis by Rockafellar is pretty hard for a beginner. It's a research monograph. I would recommend "Fundamentals of convex analysis" by Hiriart-Urruty & Lemaréchal

What tool is now used for the modeling of the optimization problem?

While the work on JuMP is impressive, isn't the fact that all major devs are from the same place worrisome?

Not sure what you mean - in case our office gets hit by a meteor?