Is there any sort of timer?
Right now, no. AFAIK the plan is that there will eventually be one.
Any loss conditions other than zero grades or discipline? Any permanently missable events?
IIRC, no and no, unless you count a branching path as "missable events". But certainly nothing you miss because of taking too much time (at least, until the timer is implemented).
If I decide to teach class, do I have the same list of potential events regardless of weekday and daytime, or are there any events that require specific day or time? Same about other activities like patrolling and paperwork and snooping.
There are some ways to spend your time that are only available on a certain day, such as watching a sexy reality tv show with some of the students in the dorm, or playing D&D with some other girls at the dorm, or watching a movie with practically all the girls at the dorm.
Also, different girls are at different places on different days and times, and progressing the story sometimes requires talking to a certain someone on the right day in the right place, but there should mostly be minor events that don't progress the time, aside from the examples given above.
But, AFAIK, after you start an activity (like teaching a class), the list of potential events is the same regardless of day or time.