Does the GET request for the new guid contain the old one?

Well, yes. But not in the header.

The POST with the telemetry data (and the old guid) is sent some milliseconds ahead of that guid request. The server does not close the connection and sends keep alives instead. When asking for a new guid, the old connection is used again. Nifty.

Werden diese Anfragen auch gesendet, wenn du Spotlight-Vorschläge und Bing Websuchen in den Systemeinstellungen für Spotlight deaktivierst?

Nein.