is there an android app that allows me to view, navigate and edit the map offline. Preferably a FOSS app. Thanks!
Vespucci: https://vespucci.io/ for a full editing experience but no navigation.
OsmAnd (https://osmand.net/) for a full navigation (and a lot more) experience but limited editing.
I don’t think vespucci can show the map offline.
Depending on what you call “the map” sure it can, see https://www.openstreetmap.org/user/SimonPoole/diary/193235 for using OSM data offline. If you want to use a background layer offline you can do that too with the MBTiles support.