Does anyone know how to retrieve the number of generated cuts in the informational callback?

Thanks for your reply. I will try to write the wrapper for the mip_cutcnt myself.
Question: Can I just locally modify the MPBWrapper.jl function on my computer?

Considering the quite simple addition to MPBWrapper.jl and the relevance of such addition for the Julia/JuMP users implementing callback functions, I believe it would be nice to just add the wrapper to MathProgBase. Is this something you would consider?

As for the Gurobi licence, I think you can get a size-limited gurobi licence for free (Software Downloads and License Center - Gurobi).