I am missing tht possibility to use the OSM Cycle map which provides topographical information. Why can't I use it with Map Factor free? Or am I mistaking?
I think, you are "mistaking". Mapfactor Navigator ist not thought to have other maps than its own maps. It's just, that MF maps are created from OSM data.
If you want to use OSM cycle maps try AndroiTS GPS Test from the playstore https://play.google.com/store/apps/details?id=com.androits.gps.test.free It's free, however it is not a navigation app, but it does display your location on the OSM cycle map and you will need a data connection to download the maps as you go as it has no offline maps.