Have you added it as a String or boolean ?

You should add width to the below class. Add that in your component css.cq-dialog-floating{}

Author interface language depends on the preference set in the logged in user. Not sure if anything to do with the page properties language !

Yes.. this is for classic UI when you use sidekick

couple of quick things1. You are using log.debug. Have you enabled the configuration to log the debug level ?? else use log.info or log.error2. How have you created your session ?? 

As @scott mentioned you can use lots of menu components like JQuery, Bootstrap etc. and develop any type of menu

It should work. Refer [1] if it helps[1] https://docs.adobe.com/docs/en/cq/5-5/developing/components/edit_config.html

http://<host>:<port>/libs/granite/operations/content/diagnosis/tool.html/_granite_queryperformanceClick on 'Explain Query'. Add your query here and see the explanation. You also attach the same here

This is really helpful !! Thanks for sharing....

This is really helpful !! Thanks for sharing....