I'll be focusing on logical graphs, especially the duality between
entitative and existential interpretations, for quite a while longer,
so this doesn't address your questions about modal logic, but you might
find it useful to compare the representations of logical operators by
means of truth tables with those using logical graphs.
You could start with the top eight entries in the section
headed “Logical Operators” on the following page.
I had been meaning to include the corresponding Logical Graphs and
Venn Diagrams — I'll spend some of my pandemic time working on that —
It looks like it would be worth the candle reviewing their properties
as representations of basic operations and going over their relative
utilities for various logical purposes.
The following two pages also contain
useful synopses of the boolean basics.