@seewhy I want to make sure that you are aware of the existing offline map feature described in the documentation. Currently, only raster mbtiles are supported so only your first suggestion is supported and somewhat imperfectly. You'd build a layer based on your previous data collection efforts and then put that on the devices. You can use PNG tiles with transparency to allow a basemap of your choice to show through.
Geo: Using the Mapbox SDK for Android is a first step towards selecting features from a layer so you may want to check that thread out. It's more broadly about adding support for vector layers, the Mapbox library is just a suggestion of how that would happen. In particular, if you have feedback on what format you would like to define your layers in, that would be really useful.