Electronic – What software was used for these schematic diagrams

As far as I remember the SPICE algorithms you do not want its internal matrices dumped on you. Also I believe for transient analysis it converts all capacitors to voltage sources (and inductors to current sources) for every time step and solves the non-linear circuit like a DC one. So there are no true differential equations in SPICE.

That said, SPICE could output the transfer function of the circuit; IIRC as a list of polynomial coefficients. This sometimes suffers heavily from rounding errors but for simple circuits it may be what you are looking for.

I do not think there is good software for this. Most people use Visio or a clone. For example, here's a library of connectors for Visio. And you can change connector colors for different wire colors, add notes for sizes, etc. Otherwise I think there's not much - this is one of those million-dollar ideas that I stare in the face and ignore on a daily basis.