Norrcomm
You can already prevent replies from re-opening Tickets with core osTicket. However we do not have the concept of auto-updating statuses, etc. That would have to be done manually by an Agent.
A Ticket Status of a Closed State has the option to Allow Reopen or not. To configure this go to Admin Panel > Manage > Lists > Ticket Statuses, click the Closed/Resolved status (for example), and click Item Properties. There you will see a checkbox for Allow Reopen. If enabled the system will re-open the Ticket when a User responds. If disabled the system will create a brand new Ticket from their reply instead of re-opening the previous Ticket.
Cheers.