There is no actual halachic prohibition to walk while reciting the blessing of Asher Yatzar. You are even allowed to walk while reciting the Shema (not the first verse).
I, at CUNY Law School, have had 2 assignments that were due on Shabbos day at 12 PM, with Shabbos commencing shortly after 4 PM on Friday. In both cases, I asked for and received permission to submit the assignments by 11:59 on Saturday night.
This past erev Shabbos, I had an optional review for a final that was scheduled to end at 4. When I requested that it be taped for me, the professor refused but rescheduled it to go from 1:30 to 3, and advised me that I should feel free to leave early. Nevertheless, I informed her that I didn’t want to cut it so close and did not attend, requesting instead that someone send me the notes. An email was sent to the entire class requesting that someone share his or her notes with me. Thus far, no one has done so, even though the final is tomorrow.
Yom Tov is obviously an issue when attending college, even Brooklyn College, which is 1/3 Jewish. Nu, so they will make accommodations.
There was one semester in college where, through no fault of my own, I had a class that conflicted with Shabbos and I had to leave early every week in the winter. That was extremely unpleasant. But in general one can avoid such classes. (In my case, the timing was changed after I had already registered for that class).
Another issue could be yichud. For example, if you are talking an exam by yourself due to having missed it on yom tov, and the proctor is the opposite gender, and they put a sign on the door saying, “DO NOT ENTER. TESTING IN PROGRESS” and no one would come in because they have such good manners. Or meeting with a professor in the professor’s office – in some cases, the door should be left open. Certainly if meeting with the dean and no one would enter her office without knocking.