Can I move the zoom and navigation buttons around?

You can move the navigation and zoom around by applying CSS to their holder divs:

map_outer, map_zoom, map_legend

and using the !important attribute to override the defaults. So, you can move the navigation arrows to the right by adding this to the map when you embed:

<style> 
  #map_outer{left: auto !important; right: 3px; bottom: auto; top: 0px; !important;}
  #map_zoom{bottom: auto; top: 40px !important; right: 3px; left: auto !important;}
</style>

The result: