Your synopsis seems to be more or less correct, from what I can gather. Here's a relevant comment in the game's code (encoded in rot13): "[n fgrc pbhagre inyhr gung vf] terngre guna 10 zrnaf vg ercerfragf (inyhr-0kssss-1) fgrcf (juvpu raqf hc orvat artngvir.)"
(The game's codebase is so large that I keep having to re-remember how certain parts work, which is why comments like these come in handy.)
As for the images on the flags (I'm simplifying here but it's basically correct): the game stores image indices in a giant list, and the flag "pip" images are stored together. E.G. there's an image for one dot, followed by an image of two dots, and so on. Normal flags don't have values greater than 9, but when glitch flags do, they try to access e.g. the 20th dot image, which ends up being a different image entirely since the indices are stored next to each other.