Is what I did considered cheating and forbidden if the manager provided me with potential exam questions before the test, and I succeeded because of them in obtaining a new position?

The department head should not have favored you by giving you the sample questions, and you should not have accepted that. Seek Allah's forgiveness and repent to Him with remorse and a firm resolve not to repeat the act. As for remaining in the job, there is no harm in it if you are capable of performing it well and carrying out its duties as required.