Rogue deletion can be set under RAPIDS > Setup page. Setting the value to zero will disable the function and Rogues will be on the system forever.

The discovery events can be set under AMP Setup > General > Historical Data retention page

Discovery events are the events about how a Rogue is detected. They can be lower than Rogue deletion, if you need Rogues to show up longer but no need of their discovery events for same period. When the Rogue ages out or deleted, their discovery events will be deleted automatically.
For your other queries:
How long will they remain? - Based on the retention value under RAPIDS > Setup page. If set to zero, they will remain forever
Will they age out? Yes and No, based on the retention value under RAPIDS > Setup page. If set to zero, they will remain forever
What will happen if I just select them and delete them? Rogue gets deleted along with its discovery events.
Will any that are still broadcasting show up again? Yes, if the Rogue is not in AirWave, they show up as new. If its already present, then the discovery events show up.
Will the delete action delete them forever even if they start broadcasting again? No, when they are seen on the network again, they will show up in Rogue list.
Apart from this, I suggest looking at RAPIDS > Setup page for Filtering options, if you see lot of Rogues which are adhoc or with low signal strength. you can set the value accordingly to show up or not, based on the security team/network team needs.
Also, setup Rogue rules accordingly as per Network/Security team needs.
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Regards
Gowri Amujuri
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