Check if you have internet access (Gateway, DNS and try to ping a domain name from the Console tools), try run the repair filesystem tool in Extended tools (this will restart system if you have NAS volumes maybe something is going on) - then try once more.
Thanks. No NAS volumes here. But internet access was, of course, the issue for second case. Proxy setting doesn't work for this update downloader? Gave the host full internet access and all fine - downloads the update, ready to be accepted.
But still can't do the local upload (which I don't need now anyway).
If you are running a very old build of DSSv6 and you want to update to the latest, try to update to build in between first before you reach the last one.