How to use own map database to display map on a website and use that map to find route and do other stuff ?
An OpenSource way to do this, which I would recommend in most cases, is using GeoServer and OpenLayers.
GeoServer can read gegraphic data from all the major databases and be used as host for the widely used standard GeographicgWebServices WMS and WFS.
OpenLayers is a JavaScript API to show your map on the webpage.