I'm new to it but know it can't handle something special I need. I want to develop functionality for LaTeX. Problem: There's something called just TeX. Then there's LaTeX. And then there's KOMA-Script. So: Which of these three is actually the "underlying engine" that drives all this stuff?
It's TeX. TeX is not just a document preparation language but also Turing-complete, meaning that it is a programming language too. Most functionality you see in LaTeX was implemented in plain TeX.