I put this elsewhere in the thread, but you can also set up bi-directional S3 replication. I haven't used it in production, but in theory it would mean you can continue write operations during failure. And those writes that are committed to the primary but not replicated when the region goes down wouldn't be lost, they'd come back up once recovery is complete (S3's SLA for data integrity is a lot stricter than it's uptime). Whether or not that is acceptable depends a lot on your use case.
Sure, though in many of S3's use-cases you won't care about writes at all, just read availability. E.g. for S3 buckets serving as canonical binary-asset hosts for CDNs to front.
Well, when the primary goes down, your write operations would get busted.
If the upstream source allows it, just write to both buckets at once. E.g. with Logstash this is trivial.