My Outlook classic is not working properly

Earlier this year I had MS Outlook classic set up -after installing Office 365 for two mail accounts:
a) BT internet and

1. b) G-mail and
   an Exchange account.
   Presently the calendar is synchronized via this Outlook Exchange acct.
   Now the severe problems which now only occur on my new Dell Optiplex Deskpro and NOT on my new Dell Inspiron notebook:
   When I minimize Outlook to run in the background I am unable to get it back on the screen and access it. When then running the Task Manager it is not visible as running.
   When then trying to restart the computer it states that Outlook is still running!?!?
   As from today I am unable to delete items through clicking the delete bin button,
   which – by the way – appears in red!?
   Also:
   Outlook also produces a large array of Synch errors in both accounts: Why – that can’t be right.
   A brief proper function of Outlook can only be achieved by 1. Repairing both accounts and then2. Restarting the computer.
   I would be very grateful for any remedial suggestions or direct help.
   Thank you