@annaceridwenx There are 2 key things about terms and the class schedules.
The 1st is what the season length is if you have Seasons. For a 28 day season, the term length is 7 days. For 14 and 7 day seasons, the term length is 5 days as I understand it. I play 28 day seasons. Also on a 28 day season length, you do not have to go to class on a holiday. For the lesser length seasons, you do.
The 2nd thing is what day you enrolled. From what you describe, it appears you enrolled on a Sunday. That means that there were be no classes on the following Monday and you get the term start pop up at 7 AM on Tuesday. The last class for the term will be the next Monday assuming you are playing 28 day seasons.
I have found that sometimes you don't get the final exam popup on the last day of class. You just get the go to class popup. Don't know why, but it just happens this way. But I have always gotten credit for the final exam in the career panel regardless of whether the final exam popup happened or not.
I try to always enroll on a Sunday and have the term end (when you get your grades) on a Monday. But if you are playing a dorm or one of the campus houses with a University Housing venue type, then the game forces you to begin a new term immediately after completing one so your next term would start on Wednesday. Otherwise, the game will force you to pack up and move out with can be a pain. I just took the easy way out and changed all the UH venues to residential. That way I can take a break until the next Sunday. Only real difference is with roommates. In a UH venue, the game will automatically assign them. In a residential venue, you have to place ads or ask them to be a roommate. They seem to play the same way once they are in.
One last thing. I have found that how much time you study makes the difference in whether you fail or pass your classes. My first sims in University all failed because I didn't study enough. Once I figured out that, I haven't had one fail since. So I suggest you have your sim study at least 6-8 hours a day and take every opportunity to study you can. I've even had one miss the last class/exam of the term (she ran all the way home to get a drink of water) but she still passed because she studied a lot.