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Context: LaTeX is a typesetting system. When compiling a document, a lot of really in-depth debugging information is printed, which can be borderline incomprehensible to anyone but LaTeX experts. It can also be a visual hindrance when looking for important information like errors.
Use entr it's a godsend! It watches when you write a buffer and then runs a command, which can be a script. Save your LaTeX often, and you never ger those errors!
Latexmk has built-in option to watch a Tex file and recompile upon changes.
For vim users, there's also vimtex, which, on top of doing what entr does, has a "quick fixes" feature that basically creates a split with a concise list of errors that's much more readable than pdflatex (or similar) output
I'd rather use TeXmacs or LyX to avoid typing in obscure commands and whatnot
A "hbox" in TeX is a horizontal box. In 99% cases when laying out text, it's a line of text. "Underfull hbox" means "I couldn't stretch the content of this line far enough, so it will look janky as f due to the increased spacing". "Overfull hbox" means "Well, I tried my best to hyphenate and line-terminate, but this word will stick out of the margin and will look stupid as f."
Most of the time this is caused by a word that auto hyphenation can't deal with. You need to add a manual hyphenation exception. I can't remember how to do that, sorry, because it's been a while and also I'm mildly drunk, sorry.
BTW I wrote my thesis in LibreOffice. That’s its own can of worms, but at least I knew how to wrestle it into submission – other than LaTeX. Set the font to Latin Modern Roman and no-one will know the difference.