WiFi or Bluetooth choice...

Hello. This is not electronics but find no proper sub-forum for it; so here it goes.

If a solar power inverter offers the feature of reporting its performance with Wifi, I believe there must be a router in the premises; does not talk directly to a 'smart' phone.
If features the reporting via Bluetooth; does it need a Wifi router or talks/reports its activity directly to a nearby 'smart phone' , with no internet service nor router in miles around as in a remote farm ?

Can a router to link devices with Wifi work without internet service provider ? Anyone knows ?

I would imagine it needs a router?, however, you don't need an Internet connection for it to connect to your phone via the WiFi as that's a local connection, and doesn't need the Internet.

Or, it could even run it's own WiFi connection, in which case you would need to connect your phone to it's private WiFi - although often that is just used to connect the appliance, whatever it is, to the existing WiFi.