How can I tell who approved or removed a candidate from a shift?

You can do this through the Export Data tab in Intelligence dashboard. Each shift is linked to an application from a candidate and that application has a status; received, approved or declined. If you export the application(s) that you are interested in, column H will confirm the status of the application and the last column on the extract (Column AN) will show who undertook this action. If this is the candidate's name then this is because either it hasn’t been approved or declined yet.