But when i search google for this guilemacs there are no definitive information for this project (as in where i download the program?).

So based on my little browsing, vim and emacs have some kind of different problems? (or are they even problems?)

Vim has the benevolent dictator who prefer supporting backwards compatibility to developing features. And Neovim try to address that.

Emacs is using a "hacky emacs lisp" and "guile emacs" tries to incorporate a scheme based improvement on the backend.