is it possible to search for a adress in openLayers?
and the other one: is it then possible to get the geoccordinate of this adress?
or maybe get the geocoordinate from the point where i click with the mouse?
OpenLayers alone does not allow you to search for an address, but you can use external web servives such as Google web services to accomplish this. Then display this information on OpenLayers.
In respect to your last question, OpenLayers can give you the coordinates of your mouse click.