The chapters in Mana Khemia roughly follow the school terms of the students at the center of the game's story. Each term is broken up into weeks, and those weeks will usually contain Events, Classes, or Free Time.
These sections will generally be driven by cut-scenes showing conversations between the various characters. There might be a few things the player has to do to complete the course of events before the next week begins.
When the player is given the ability to roam campus during an event, it is still possible (usually) to visit areas of campus unrelated to the event, and it may be possible to visit Off Campus areas. Generally, time doesn't pass in any normal sense while on campus, so it's possible to do almost anything during an event section without finishing the week until the conditions to finish that event are completed. This means that it's possible to synthesize items, buy items in the various stores around campus, and possibly even explore and find new areas and items Off Campus, as long as the areas in which these things are done are not part of the event themselves (some events will trigger when entering certain areas, so entering the Workshop, for example, might trigger the cut-scene that ends the event, and the week).
Classes are usually available in the Student Affairs building when they are in session. Some classes are required, others are optional. As the game progresses, there will be more choice in the matter of what classes the characters can take.
Usually characters will head straight to class after signing up, and the teacher will give a short lecture and an assignment. Assignments can vary, but usually involve creating a new item of some sort or defeating a specific enemy.
Classes are graded based on the performance of the tasks involved. The more points you receive for your classes, the more Free Time you'll receive near the end of the term. If you receive too few points, you'll receive Detention, which involves completing more tasks for the teachers.
Free Time weeks don't have specific requirements for completion. You can take jobs and talk to your party members to continue Character Quests. This is also a good time to explore the Off Campus areas, synthesize items to expand the characters' Grow Books, and find new recipes. It is also possible to just go to sleep to complete a Free Time week.
It's usually best to grab all of the jobs available in Student Affairs and finish those before starting any Character Quests. Once you feel satisfied with the progression of your characters, start one of the Character Quests by talking to that particular character. Finishing the Character Quest will finish the Free Time week.