Correct; and your argument is one that everyone loves to make. Although, during times of such "bigger problems", having access to a global medium of exchange, such as Bitcoin, would be a catalyst for faster rebuilding. So I do think it's worth considering.
Perhaps, but physical fiat cash will also be a medium of exchange and it isn't reliant on computers and the internet.
My proposal is to simply look at the difficulty and compare it to what was previously in the blockchain. If it deviates by a margin, we know that something has happened, and that a significant part of the network is no longer available... so what now? Some scenarios can be modelled - and the network can adapt based on our best predictions of these situations. Ie. it can increase the block time by a margin... and only accept that parts of the network are indeed not coming back, after a reasonable amount of time.
The difficulty only changes every 2016 blocks which is targeted to be 2 weeks. Nodes would not be able to detect that miners have dropped off except if blocks simply have not been found in a while. Even so, if a significant part of the network dropped off, block time intervals may not indicate whether the hash power has dropped off. If 50% of the miners could no longer connect, block times would still only be 20 minutes between blocks, which is not infeasible to see now. In fact, we sometimes have block time intervals of over 1 hour.
Not necessary.
How so? I have tried creating a node which connects to every other node, and it failed miserably. It ran out of resources. There really would be no way for every node to know about the status of every other node in the network without connecting to those nodes.
Then why use Bitcoin at all? Why not just trust the banks... you know, banks lying to us and forging documents is arguably equally rare, right?
If the internet were to go down and thus Bitcoin would no longer function, so would many bank systems. Most use computers now and connect via the internet to get balances since in reality, most money is digital, not cold hard currency. Banks know that there is a possibility, however slight, of the internet going down and their systems thus failing, but they don't cater to that scenario because of its unlikeliness. There are infinite possibilities and failure scenarios, but most of them are extremely rare events, and thus people don't even bother to solve them because it is wasted effort, and thus Bitcoin should not do something about a failure scenario that is extremely unlikely
There are also projects in the works to bypass internet censorship and to also be able to use Bitcoin without connection to the internet. We can use radio to transfer the data for Bitcoin as well as many other methods to move the data around internet censors and even internet outages. There are also other projects like Tor which bypass those internet censors anyways.