In iOS app I have a widget, a menu that is part of all my screen. Is it possible in Android to nest activity into other activity, and so widget in outer activity is able to see in inner activity? I want avoid any code duplication, redundancy.
Yes, but you need to use fragments. An activity cannot contain another activity. About the navigation components, you can always check the design support library and use the tabs component or the navigation view.
Email codedump link for Container view controller in Android?