Dear David,
Greetings! Thank you for posting in Microsoft Community.
I'd like to help you, please let us cooperate, we can work together to narrow down and resolve the situation.
I suppose the "document section" you mentioned is the Document library in a SharePoint modern team site. If not, please feel free to correct me.
1.Regarding "I would like to create "private" folders for each individual participant (which only he and of course the administrator can access and edit, the others do not have to view the content)."
You can set unique permission for each folder in the Documents library, only share the folder with individual participant.
Select a folder and click the 3 dots next to it, choose Manage access > then click the 3 dots and click Advanced settings > click Stop Inheriting Permissions > then click Grant Permissions, enter email address of an individual participant, choose a permission level such as Edit, and click Share. Repeat these same steps for each folder in the Document library.
2.Regarding "The same thing I would like to do for the lecturers, but in this case, however, the content of one lecturer can be visible to others, but not editable.".
You can repeat the same steps above to set unique permission for each folder for lecturer, when you grant permission, firstly grant Edit permission to lecturer, and then grant Read permission for others.
I hope above helps!
If you have any update or you need further help, feel free to post back, I'll be glad to help you further.
Thanks for your time and cooperation! Hope you have a nice day, stay safe and healthy.
Sincerely,
Tina | Microsoft Community Moderator