Google Polymer for Android native app

No, you cannot use Polymer to build a truly "native" Android app. Although there are frameworks such as Phonegap which would allow you to build an app using web technologies and then compile into an Android app.

If your goal is to make an app that follows material design patterns, I suggest you get started by reading the official documentation on the subject: Creating Apps with Material Design

If you are into native Android then you should use Android Official Appcompat Library(which is default) but it lacks backport of some Mateial elements and features( Official Tutorial). if you really need to implement the elements which Appcompat lacks you can use any third party librarie like MaterialEverywhere or this or you can find here if something is really availabe in the world.

Yes, you can make native mobile apps with Polymer, thanks to Polymer Native.

Polymer is a JavaScript Framework that implements web-specific standards for the front-end.

And JavaScript is not the native language of Android so Polymer cannot be used to build Native Apps (using Java) using Meterial Design.

But on the other hand you can build entire applications using HTML5 with the help of some technologies like Cordova and PhoneGap.