> Can you use bitcoin without the internet? Can you use bitcoin without someone else mining and being allowed to connect to these entities?

The answer to both is, simply, "no".

All cryptocurrencies (not just Bitcoin) are incredibly reliant on the availability of unrestricted communications between all participating parties, including miners. Where those communications break down, the cryptocurrency is likely to become unreliable or entirely unusable.

(As such, Bitcoin is an incredibly poor choice if you're planning for some sort of apocalyptic scenario -- it's likely to be one of the first things to stop working.)