Is it possible for me to edit the suspended tickets view? Further, can I have business rules 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. There is a third-party integration that allows for more complex management of your suspended tickets queue, known as Shredder, though the app is not officially supported by Zendesk.
The suspended queue is a default part of Zendesk Support and will be shown to administrators and any agent with access to all tickets in your account.