1) It would have to be a really bad day for the internet globally if all of the eligible nodes at any time are seeing latencies approaching 60 seconds.
2) Eventually yeah, but then that will likely also mean the network is dead and there aren't any client nodes coming online to make transactions either. Same as if all the miners went offline never to return.
1) Of course, steady state you don't expect to see latencies like that, but connection interruptions and crashes do happen. How does a crashed node, which has been disconnected for, say 1 day know how to resync and who the correct nodes are to listen to?
2) What I mean is that if you have set of N nodes, who propose future nodes M from the subset of N, nodes going offline will lead to 0 eligible nodes if M must always be a subset of N.
Well, any eMunie client, new or offline for several days, can fully sync even when only non-service nodes such as a client only. Some of the client only also have the full ledgers. I proved this by syncing a new client with just the client only faucet as the only active node.