Neither of these are currently a feature in osTicket.
The new ticket alert you could get around by creating a mailing list for the department manager.
On that mailing list you would put the manager and the admin.
Then when the Manager (which is actually a mailing list) gets the alert a ticket has been opened it will update both of them.
As far as a close alert, I cannot think of a good way to do this as Close alerts are not a feature. I think that you would have to alter the core code to do this.