Android: I cannot remove elevation / shadow on my toolbar

You can do that with an easy step. Don’t remove the android.support.design.widget.AppBarLayout from your layout, instead add the attribute app:elevation="0dp" to it. Your final layout will be:

<android.support.design.widget.AppBarLayout
            android:id="@+id/appBarLayout"
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            app:elevation="0dp">
            ...
</android.support.design.widget.AppBarLayout>