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Hi,
thanks for asking. Please find my answers below.
 I tried removing the action/behaviour from the Behaviour 
Construction Kit, but that didn't do it. So, how can I remove these 
annoying double entries?
  The actions in the BCK do not turn up anywhere else unless you make 
them "global". Other than that, the only way to permanently add 
Behaviours is to save your own Behaviours. Those are saved to ~/ 
Library/Application Support/Remote Buddy/Behaviours/ by default.
Changes you make to the contents of that directory only take effect 
after a restart of Remote Buddy.
 Another question that came up for me is, how do I properly add a new 
action to an existing behaviour (Aurora in this case)?
  1) Go to Preferences > Mapping > The App You Want To Add An Action For 
(here: Aurora)
2) For the button that you want to have a custom action be executed, 
click on the popup in the table then choose "Custom Actions..". You of 
course can later assign that action to other buttons of your choice.
Best regards, 
Felix Schwarz