It can detect cycles. From a quick look at the demo of this tool it (slowly) generates some garbage text after which it places 10 random links. Each of these links loops to a newly generated page. Thus although generating the same link twice will surely happen. The change that all 10 of the links have already been generated before is small

On itself it doesn’t auto update, you do get a notification in the app if your server is outdated.

You can setup watchtower or something similar to update it but it is discouraged due to the active development