Hi Tomasz,
Generally speaking the upgrades should work even on customized projects, it all depends on complexity of customizations and these specific customizations should be transferable to another version because as far as I know there are no plans on major redesign or braking changes in pages.
As for your oringinal question to customize the context menu in the tree you will need to customize two controls yourproject\CMSModules\Content\Controls\ContentTree.ascx and yourproject\CMSModules\Content\Controls\TreeContextMenu.ascx .
The listing view extension customization might be easier as all you need to do is create an extender for the UI interface with class that covers the logic and new unigrid actions. There is even a page in documentation for that:
https://docs.kentico.com/display/K9/Creating+extenders+for+module+interface+pages