How to create a floating touchable activity that still allows to touch native controls outside of its borders?

Set a Dialog theme on the Activity in your manifest. For example:

android:theme="@android:style/Theme.Dialog"

Then set the following Window parameters in onCreate():

public void setWindowParams() {
    WindowManager.LayoutParams wlp = getWindow().getAttributes();
    wlp.dimAmount = 0;            
    wlp.flags = WindowManager.LayoutParams.FLAG_LAYOUT_NO_LIMITS |
                WindowManager.LayoutParams.FLAG_NOT_TOUCH_MODAL;
    getWindow().setAttributes(wlp);     
}