Hi,In editable templates there is no Design mode available.Instead you can use component policy,refer below urls:Creating Page Templates AEM Developer Learning : Dynamic (Editable) Templates in AEM6.3 : Part-2

you can use PageMgr api : pagemanager.delete(resource,boolean)  , where resource will be your custom package.

Is the image present in publish ? Are you able to access the image in author?

Hi,You can try implementing EventHandler/Listener and handle PageEvent. This will capture all events on a page and you can do your custom logic.It will be a costly operation though as eventhandler will be triggered for every modifications.