I'll try and answers some questions you asked.
Which direction? Towards middle six rooms at the start, checking out how many math notebooks spawn (not collecting), eventually reaching cafe. I grab a lemonberry on the way.
Visit Mr Mix? I usually do this once when reaching the cafe, managed to snag all 10 math notebooks without visiting before.
Items? Towards the beginning: Lemonberry, NUTS bar, blue key, magnet (if possible). Towards the end: Chocolate chip muffin, lemonberry (new), NUTS bar (same), magnet (same or eventually found).
Skip rooms? The six middle rooms mentioned at beginning, otherwise; while making your way towards a specific end of the school...I never skip and collect notebook if possible.
Time for notebooks? I never used a calculator for first 7 math notebooks, gotta practice addition and subtraction. Saves time. Extra time if you lemonberry or muffin Viktor away from middle.
Staining Viktor? I usually do this twice before the final exam. One before collecting early notebooks, not in middle six rooms. One before rushing notebooks 8-10 on one end of school. I lemonberry Viktor as he's talking before final chase. Also, I rarely juke Viktor as I use warp doors.
Final Notebook? Luck of exam numbers for calculator plus fast fingers. Used to have enough time as exam could spawn on one end and you could force Viktor to backtrack towards bathroom and back, allowing plenty of calculator time, not anymore... That one thing cripples my current strategy, haven't been able to beat it since (suggest using warp door with two other doors while Viktor's talking before exam and collect 10th notebook in two rooms close to vending machine where alarm clock used to exist).
Gas mask? Never used it nor tested whether it tricked Viktor or not, I'm guessing yes. Guessing...
EDIT:
Current Route (complex): Not exactly good as it goes back and forth too much.
Ruined Route (optimized, but flawed): Thanks to exam location at start.
I don't think tracing these maps help; my best run on 0.0.9 Brainiac was 5/5 exam questions answered correctly, but died to Viktor during completion delay. That was with the best set up (lemonberry Viktor when he's talking at room door, run to warp door from one of two rooms labeled on current route, place magnet on 1st classroom door, get good exam numbers). Even had a 2nd magnet to block another door.
Brainiac Marzia is more doable than Brainiac Viktor (and doesn't require a calculator to complete the exam in a timely manner, just elevator number memorization).