I’m not sure exactly what you want to do, but I’ll try to answer some of this:
That code will just give you a slippy map for your website. That map is made up of tiles, which are just bitmap images. So there’s not really any way to ‘interact’ with particular map objects.
If you want to interact with gas stations for example, you would have to get the actual OSM vector data for these.

There’s a few different ways to get this .osm data:
You could use XAPI to download everything with a particular tag within a bounding box. http://wiki.openstreetmap.org/wiki/Xapi
Or you could download a Planet.osm extract, then use Osmfilter to extract objects from that file. http://wiki.openstreetmap.org/wiki/Planet.osm http://wiki.openstreetmap.org/wiki/Osmfilter

Then once you have the data, it depends on what you want to do with it. If you want to have a slippy map on your webpage, with icons to click on etc, then you can use OpenLayers. eg something like this example: http://wiki.openstreetmap.org/wiki/Openlayers_POI_layer_example