(1) Are these shutdowns a worldwide phenomenon, or is it just me (in good old Europe) having difficulty?
Worldwide. Sucks big time.
(2) Are they planned (some sysop/developer/whoever making some important changes etc.) or do they happen accidentally?
Both. We've had some major database updates recently, but we also have occasional problems. A total crash without apparent reason, and this time MySQL max_connections problems, even though we're already at 250 and use pconnect (persistent connections).
(3) If they are planned, could the community of users be given notice when and approximately for how long Wikipedia will be down?
When there's scheduled downtime, it is usually announced on the mailing list. Let us know if you find someone willing to run a complete read-only mirror, that would help.
Regards,
Erik