Deactivating or deleting someone signs them out immediately. The last active administrator cannot be demoted, deactivated or deleted. The Google column is the address that account may sign in with - a tick means Google is linked; changing the address unlinks it.
Categories are shared by everyone. Renaming one updates every task using it; deleting one leaves those tasks uncategorised rather than removing them.
Shows every public task, plus the private ones you created or were assigned. Other people's private tasks are visible only to their creator and assignee, so they don't appear here.