To change the hamburger icon, just create a new icon (e.g. ic_my_dark_menu) then assign that to your action bar:
actionBar.setHomeAsUpIndicator(R.drawable.ic_my_dark_menu);
Or, you can tint your existing icon, if you'd rather do it this way:
Drawable drawable = ResourcesCompat.getDrawable(getResources(), R.drawable.ic_menu, null);
drawable = DrawableCompat.wrap(drawable);
DrawableCompat.setTint(drawable, Color.BLACK);
actionBar.setHomeAsUpIndicator(drawable);
To change amount of space between your action bar title and the edge, just edit your toolbar layout (res/layout/tool_bar.xml). For example, you can add padding like this:
res/layout/tool_bar.xlml
<android.support.v7.widget.Toolbar
...
android:paddingTop="16dp" />
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