You should think of the sequencer layer as a shared log abstraction along the lines of the Corfu project from Microsoft. It is distributed and replicated, with the scheduler layer reading from their local copy. Stalled scheduler nodes do not block writes in the system.
Yes --- the current version of Calvin (in the Yale research group) does not have this limitation. We're actually not sure which paper you're talking about, but either way, it's not fundamental to the Calvin approach. In general, if a single server in a replica fails, the other servers within the replica that need data from the failed server can access that data from one of the replicas of the failed server. (We can't speak for FaunaDB, but like the current version of Calvin, it is unlikely they have this limitation.)