Important questions about rule and more

Take this:

Can I make a field readonly for user input in DevOps, but still change it via rules?
Yes, but with limitations. You can make a field read-only using rules, but you cannot update and make the same field read-only in a single rule execution. 

Can I change the iteration path and the state by rule?
For state, yes, you can change the state of a work item using rules. You can also restrict transitions, make fields required or read-only based on state changes, and apply conditions based on user roles.

For Iteration Path, no, you cannot change the Iteration Path via rules. This field is of type TreePath, and Azure DevOps does not currently support rule-based changes to it. This limitation has been acknowledged by Microsoft, and users are encouraged to submit feature requests.

Do I really have to have the Closed state on every board, even if users are not allowed to pull a ticket into Closed?
Yes, the Closed state is part of the default workflow and maps to the "Completed" category, which is used by Azure Boards to determine visibility and reporting.

However:

You can restrict transitions to the Closed state using rules.
You can hide the Closed column on boards or limit visibility by customizing board columns.
Work items in the Closed state automatically disappear from boards and backlogs after 183 days unless queried explicitly.
So while the Closed state is technically required for proper workflow categorization, you can control how and when it's used or displayed.