> I still have to understand openstreetmap mapping solutions. It's named open, not free, so I guess providing your own server with osm data would work. Only with FreeStreetMap the data would be infected also.
I'm not sure what you mean with "free"/"open". The OSM licence has a share-alike part if you merge your own map data with OSM data. If you just have a map and put points on it, it'd be fine.