How to make sense of font metrics?

Here is an attempt at answering item 2, assuming you are using a traditional TeX or pdfTeX format with TFM-based fonts (not XeLaTeX or LuaLaTeX):

For plain TeX, there is testfont.tex. For LaTeX, the fonttable package does something similar. For context, there is the \showfont command.

PS: I have no idea how to answer anything else; 1 and 3 are much too general for an answer that is shorter than a medium-sized book, and I know nothing of 4.