Is it possible to edit the suspended tickets view and to create business rules that take action on tickets in a suspended state?
As suspended tickets are not legitimate tickets in your account until they are recovered, it is not possible to edit the conditions for this view or natively create business rules to take action on them.
The suspended queue is a default part of Support and is shown to admins and any agent with access to all tickets in your account.
However, Zendesk created an app that allows for the bulk deletion of suspended tickets. For more information, see the article: Installing and using the Bulk Delete app.