Hi Lusi,
We appreciate that you posted back and confirmed the scenario with us.
Per your description, you want to create a site and your school teachers and post for their students exams and results. And every student can also use their accounts to access exams, results and grades.
If so, as I mentioned above, you can create a SharePoint site, then the teachers can upload exams files to SharePoint library, and they can also upload exams results to SharePoint list.
Then you can give edit permissions to students to access the exam files stored in SharePoint library, students can access the exam files and finish the exam.
Then you can give view permissions to students to access SharePoint list, then they can access their exam results in SharePoint list. For more details about permission, you can refer to this article: SharePoint site permissions.
However, you mentioned that you only have Microsoft account, if so, we’re afraid that you may not have permission to use SharePoint Online. As I mentioned above, if you don’t have SharePoint Online license or plans, you may not have permission to use SharePoint Online Service.
For your reference: Compare SharePoint Online options.
So to answer your question, if you just have a Microsoft account, you may not have ability to access SharePoint Online Service and create a SharePoint site.
Your understanding and patience will be highly appreciated.
Best Regards,
Sukie