The case of the missing laptop is still unknown at this point and it can't be said definitively that it has anything to do with Nick and/or Vinny or that that getting back at Cathy in some way had anything to do with it. Cathy is likely no more than the unfortunate chosen victim of whoever posted that pic. I don't see there being any deeper reason for Cathy being the person who's picture was posted, it's simply that the cast of teachers/faculty in this game is small and if we had more than just 2 female teachers then it could have been any one of them, but since we don't, this is why Cathy was the victim.
As far as the DIK secret code is concerned, from what we know of it, it's basically a pact to keep something that either is or could be potentially damaging to them a secret. Jacob invokes it to ensure that nobody outside of the DIKs ever brings up what Derek or the MC did with a teacher because of the ramifications this could have for both them and the DIKs as a whole. Rusty invokes it so that after telling his brothers the details of his conversation with Cathy that nobody outside of them knows what happened. If Vinny was expelled for dealing drugs, then someone like Nick could have invoked it so that nobody knows from that point on what happened with Vinny, and this would extend to new members of the DIK fraternity. Vinny may not be part of the DIKs anymore, but the DIK code is a pillar of the frat and the DIKs will stick to their secrecy.
A blessing for the modern day man! But seriously, that future MC stuff is garbage. I prefer to stick with the present because whenever we switch to the past or future it pulls me out of the story and reminds me that this is actually MC's story and not mine. I take my role-playing seriously in games. While playing I like to forget about the outside world and fully immerse myself in the character I have created.
