As far as I know, you’ll have a last syched copy in your cache. Test it with no internet con! Try to export your data without internet.
I’m using vaultwarden for like 4 year now, but on my personal server at home. Btw a raspberry pi is enough to run vaultwarden.
You could take a look at reverse proxys and dyndns services (like duckdns -> free). I started like this. Now I have my own domain, but that is not mandatory!
You can take a look at FFUpdater on F-Droid. There you can see different browsers for android and information about the features they have.
I’m useing mull.