3Blue1Brown has a fantastic video on GPT that I'd highly recommend called "But what is a GPT? Visual intro to transformers" [1]. You'll need to have some background in mathematical reasoning, but not too much. He does a great job of drawing pictures to show the mathematical transformations that happen under the hood.

[1] https://www.youtube.com/watch?v=wjZofJX0v4M

There are videos on youtube where you can see how the token generation happens like an algorithm

The process itself is quite simple. I think everybody is surprised how well it works because it's the power of statistics + great data

Unfortunately, it can't reason at all and would need other AI fields in order to be able to tackle some other simple puzzles

I'm not too sure. When I first encountered LLMs, I decided to try implementing one from scratch. I didn't get far, because it's difficult, and I only have finite time and energy. Still, it was the process of trying to implement some basic stuff that gave me an idea of how they work under the hood.