Most of the glitches in the game are performed using the Punch Card. Every time you use the punch card to skip a mettaton cutscene (cooking show, news show, opera cutscene), the game still thinks you're in the cutscene and doesn't let you use your menu (so you can't use the punch card). Going from the water cooler room to the bridge room gives you your ability to use your menu back, so the runners will do that after every skip that takes away their menu.
Yes, that's allowed. Many runners including me use AutoSizer which does basically the same thing, so I would recommend that one
What did that guy ever need Madeline for
I feel like the game is already pretty well optimized for speedrunning, so there's not much that seems required to me. You're the creator of course