My school started this RPing club, but in my school right now only 2 people know how to DM and do it effectively, including me. As the teacher running the club knows nothing about Pathfinder, it seems that I will have to get some of my friends who play Pathfinder during lunch to DM for other groups. How can I teach 3 people how to be a DM in 15 15-minute sessions?
Strip down most of Pathfinder
Only introduce a handful of classes and mechanics. You can then introduce them at a later date, but for a first session, if you simply prepare a handful of fighters, rogues, sorcerers and clerics - or something with that sort of spread - you can give people an idea of the 'flavour' of Pathfinder and Fantasy RPGs in general.
More complicated concepts like Vancian casting or less vital parts like skills can be avoided for now, or mentioned in passing then glossed over. It's easiest when teaching a new system to a new player to cover the basics ("This is how you attack", "You've taken damage - subtract 5 from your hp", "You cast a fire spell and kill a goblin") that the players can understand quite easily from video games, then focus on the strengths of PnP RPGs - the interactivity and roleplaying aspects.
Later on, if your players come back for more, you can introduce more classes, add skills, flesh out other subsystems you've mostly ignored, and generally expand the game over time until it's 'proper' Pathfinder, assuming you want to! The group (or you) might enjoy the easier version as much as, or more than, the full version, in which case it's easiest to just leave it as is.
I have had personal experience with running a (lunchtime) RPG club at school. We used 2nd edition D&D, with the only experienced player being a cleric, and then adding a Ranger, Thief, Paladin and Invoker. We only played from level 1 to level 2, but it worked well. We ignored non-weapon proficiencies, I made all the characters beforehand with the other veteran helping me, and a good time was had by all. We never needed to add more of the system later on, because the stripped-down version was quicker (very important with shorter play sessions), and I learned a lot about keeping play moving for a group with players that don't all get on well.
Thinking of this as a one-off interdimensional travel lead me to think about a (remarkably equivalent) conceit being the center of Harry Potter and the Natural 20. In short, it tells the hilariously funny fiction of a genre-aware 3.5 wizard dropping into Hogwarts and steadfastly maintains the truth behind each universe. The imported little Munchkin, Milo, indeed works to 3.5 mechanics in the "real world."
For your thing, therefore, don't try to "merge" them. Layer the systems. Each character comes with their own system and imparts those effects on the world. Preferably as literally as possible. Treat readings of abilities as "true" rather than as mechanical abstractions designed to represent a world. Of course, use the exact same rules for the enemies. You'll want to think through the abstractions from a system specific point of view: "What does 3.5 damage mean in context of WoD, treating things literally" and so on and so forth. While this would be tedious to pull off in any kind of sustained campaign, the incongruous juxtaposition of systems could be a hilarious and fun farewell to arms.