Learning Route
Assuming you've played the game casually before, the best method for learning the route is to copy the WR run off the leaderboard, or use a walkthrough. I like using notes for memorizing my route. Speed Guides Live is a very useful LiveSplit component for writing notes that display in each split. I assume most will want to write the notes themselves, but here's mine anyway. https://pastebin.com/uuCx6rJ1
Movement
For quickly selecting actions, you can either use the Action Icon Chooser or keyboard shortcuts. T - Talk U - Use/Grab I/Space - Inventory L - Look (useless) W - Walk (useless, except for easter eggs)
Right clicking in the Inventory screen will set your cursor to Use.
Of course, you must hit Escape after examining or interacting with any item to skip cutscenes/animations, but exits can't be skipped, as they lack an animation. In some areas, you can save time by interacting with what ever item is in-between your starting location and the exit. Examples 1 and Examples 2.
Hock-A-Loogie
Principal McVicker, who you must fire a Mega-Loogie at in order to progress, always shows up 30 seconds after launching the minigame. You'll almost always have enough time to rack up 10 hits if your aim doesn't suck.
When the mega-loogie hits McVicker, a short scene plays where he yells at the duo then runs into the school, before the minigame closes and resumes the main game. Instead, you could save a few seconds and manually close the minigame by hitting Esc after McVicker finishes speaking. If this didn't work, then you're closing the minigame too early.