Unfortunately not, as the device cannot and must not decrypt HDCP. Copy protection. Only TV sets, projectors and monitors can decrypt this signal.

Theoretically yes. However, I don't know whether the Swisscom box uses HDCP. If not, it should work... If yes, then the Swisscom box would block the recording. You could get round this with an HDMI splitter, but I think it gets complicated from here.