Can I turn my phone off or work with other apps while Arrive/Depart is timing?

Yes.  Arrive/Depart records your arrive time then your depart time.  If you shut your phone off or open another app, Arrive/Depart is unaffected.  You just have to remember to go back to the app to record your depart time.

I forgot to record my depart time when I was finished.  Is my record for that event useless?

Definitely not.  When you do finally tap “Depart” you can go into the Service Records, find that event, then edit the time as often as you’d like. No problem.

I want to keep my records for a particular service but since I’m not involved with that company anymore I don’t want that service to clutter up my service wheel on the home screen.  Can I remove just the service on the wheel without touching the records.

Yes.  Go to  more > Delete Options and follow the instructions for # 1.  By deleting the service (or location) here the home screen wheel will be cleaned up but all the services will still be available for viewing or editing in the Service Records section.