Additional chat-related features and issues within Microsoft Teams for Education
Hello Talie,
Welcome to post your query here.
As per my knowledge, it's not feasible to export the conversations in Teams directly. As a workaround we can copy the entire conversations, then paste them to Word, OneNote, or other apps. Also for the single chat, we can share it to Outlook via click Share to Outlook option after you click more options of that specific chat. Or other workaround is that capture the screenshots of those conversations, then save it as .PNG, .JPG or other type file.
Actually, for your first and second query, the admin have the permission to run the content search from admin center, there admin may be abled to export the needed information. So if you are not the global admin in your organization, please do involve your admin here to go ahead. For the admin reference: Conduct an eDiscovery investigation of content in Microsoft Teams.
Have a nice time.
Regards,
Rudy