9s rear deraullier with 10s chain I have a 9s rear derailleur in a 10s transmission. It works fine, but I have concerns about if this configuration could produce problems in the long term.

I know the 10s chain is narrow compared the 9s chain, but it fits properly in the wheels of the rear derailleur. But maybe I'm not taking into consideration other aspects.
If your cassette is 10 speed, you need a 10 speed chain. The derailleur will be fine.