How and where can I track students who defer studies?

If you have a form tool (Form Assembly, Conga, Formstack, etc.) or web-to-case form (with some customization to the Case object) would be the easiest to setup. If you are using Community Cloud, an LWC/VF page would work. You could either have them update their Program Enrollment directly (maybe coupled with an Approval process), or create a new child object with those changes and your team updates the actual course connection records.