un-synching a computer
If I were to sync a computer in a classroom to my library on the Zotero server, how would I remove the library on the classroom computer when finished? Is there a way to delete the libraries on the classroom computer securely without deleting the data on the server and on my personal computer?
After that, pretty much nothing can happen, because the computer can't sync with your account -
I think I'd just manually delete everything in your library and empty the trash.
Are you on a University campus? Can you not login to a classroom computer with your own account? Usually that would have your Zotero profile (including library) stored on it.
When I delete the library on the classroom computer, am I using the Zotero trash icon, or the desktop trash icon?
select all items (e.g. using ctrl+a)
then right click and select "delete selected items from library"
confirm
then empty the Zotero trash and confirm again.
As for the first question - you don't need to be logged into the website to sync, no. It's both necessary and sufficient if the login information is in the sync preferences of your Zotero.