You definitely can screw up the homework chain, my most recent game it never got beyond the offer to help with homework and that chain is sitting at "wait for an opportunity" even though I have just about finished the rest of the available content and ran out of classes to attend some time ago.
I have managed to not see MARTIN in my game either. I know I am giving up any Maria and Vanessa scenes at the moment but I was playing the new version without looking at the walkthrough. Money seems to be a problem in this version of the game as I played it as the cafe is the only source and the time sits on top of a lot of other events, while there are huge chunks of the weekend where nothing happens. I never met the janitor though, just found the key in the closet so I may have missed some path there. Plus Bill doesn't really have much to do yet. Each spycam takes 6 days of work, or 5 and your mom's money to purchase, so that is close to 2 weeks game time just for that when there are a lot of other things needed to buy as well.
I've had some hard lockups as well. Go to the gym at 20:00 for the first time and purchase a membership for $100 (even though the offer conversation said $150 and a girl gets in free) don't have anything to do yet so go in the locker room. You may have a spy icon, or you might have to wait an hour, I can't remember. Click on the icon and there is no one to spy on and no hourglass to move time ahead. I needed to force close out of that one. Go downtown (where you meet for drinks) if no one is meeting you, open your phone and do a few things, close the phone and the UI is missing so you can't get out of downtown.