I'm new to Cordova(PhoneGap) and it is not clear for me if the result built package includes the html/js/css files or if I need to have a server hosting it?
I would like to have the html/js/css files updated automatically when I change them, would that be possible in Ionic+Cordova approach?
Basically I want the app to be able to work offline but to update its contents whenever there is a new version available. What would be the best approach to achieve that?
Yes, all the HTML/CSS/JS is bundled into your apk/ipa file as documented here, you don't need to have a server hosting it.
As far as the updates go, one option would be to release your app via Microsoft AppCenter, then you can use their CodePush functionality to perform updates.