TeX (plain TeX, not LaTeX) has phenomenally good logging and error messages IMO — everything you need is there, each error message comes in a “formal” and “informal” form and points you to exactly the place the error happened, and TeX lets you fix things on-the-fly without restarting the program. All this of course assumes you use TeX the way it is described in the manual (The TeXbook). The experience is opposite with LaTeX, so I find it worth giving up all the convenience of LaTeX just for the wonderful experience with TeX.
As for “the TeX language”, there is no such thing. As Knuth has said many times, TeX is designed for typesetting, not programming. Sure it has macros to save some typing, but if you're writing elaborate programs in it (as is nearly inevitable if you're using LaTeX) you're doing something wrong. Knuth said:
> When I put in the calculation of prime numbers into the TeX manual I was not thinking of this as the way to use TeX. I was thinking, “Oh, by the way, look at this: dogs can stand on their hind legs and TeX can calculate prime numbers.”
But of course LaTeX does every such thing imaginable :-)
..."virgin" TeX...knows just primitive commands, no macros. Plain TeX is the set of macros (developed by Knuth) which makes TeX usable in everyday life of a typist. ... The available commands can be classified into primitive commands and macros. ... The "virgin" TeX knows only the primitive commands. ... Formats (plain TeX, LaTeX, etc.) extend TeX's vocabulary by defining macros. ...For example, plain TeX defines macros \item, \rm, \newdimen, \loop, etc. Plain TeX defines about 600 macros.
Yes of course; see this answer I wrote about typesetting with “virgin” TeX: https://tex.stackexchange.com/a/388360/48 (it's not easy). “Virgin” TeX is never (and was never) used by typical users, and is used only by the system administrator (or these days, the people behind the TeX distributions) to pre-load formats (like plain or LaTeX).
Knuth wrote both the TeX program and the “plain” set of macros; when you start `tex` it is with `plain` that it starts up, and The TeXbook describes both the TeX program and the plain format without being careful to distinguish what comes from where (you have to look at Appendix B to see the proper definition of plain.tex), so when we speak of TeX as Knuth intended/imagined it to be used, it is plain TeX that is meant.
