About the UI: that's understandable, but I wanted the whole thing to feel more like a real computer system than a game, and I think a little bit of friction and inconvenience (emphasis on "little"!) helps to sell that fantasy. Maybe the message could be worded a little better though, I dunno.
About the puzzles: if nothing else, I'm glad you could get through the story despite not fully getting the logic! I'll take that as a sign that the hint system is working properly.
I'll leave you the full logic for 0000, fully rot13'd:
Guvf bayl hfrf gjb pbqrf: ke, juvpu zrnaf ebgngr gur yrggre sbejneq va gur nycunorg, naq kq, juvpu zrnaf qhcyvpngr. Fb (keo)eb(kqf)(kej)e(kqq) -> pebffkeqq. Gur chmmyr vf nobhg ernyvmvat gung bapr qbar jvgu gung, lbh unir nabgure ke pbqr, fb vg orpbzrf pebffrq.