Creat my own editable map from openstreetmap for app and web

Hallo, I want you to show me how to edit Openstreetmap to add street and house No. in a map editor . then host (save) map tiles in any format on a Server to use it in an apps and webs. I mean to use Openstreetmap or onther maps as base to make my own map for some cities and to be able to edit streets and House no. any time i need it. Some terms mybe helps: openstreetmap, Vector tile, map tiles, map editor . map server . adress search in a map.