The Waze search engine pulls data from many different sources, but usually either from its own data or from Google Maps. So when you search you can end up with the same place from multiple sources. You can only suggest an edit for places that have been created in Waze. There is no ability to edit the location when it pulls up a third party location because Waze is just presenting the info.

If the list is incomplete, it could mean that Waze thinks you are to far away from the street or the street has not yet been added to the map.