For what it’s worth, as of yesterday there is a new version of Syphon Recorder. None of the Syphon capture stage has changed, so I doubt it will fix your problem.
1. okay – something strange is definitely happening.
2. If you see nothing on the Billboard in QC then you’re not doing it right. The Billboard needs to be layered below the Syphon Server. The output of the Video Input patch should be connected to the Billboard’s Image input (and not to the Syphon Server). Once you can see the image in the QC viewer it should also show up in Syphon Recorder (with the dimensions of the QC viewer window). Try recording that.
5. I would guess yes but it would really be worth trying it if you can get your hands on one before you buy.