shiftscreen only enables you to use the full size of a monitor and control the monitor while you do other stuff on your iPad. That's why you will always need a cable (for example USB-C to HDMI) to connect to the monitor, software like Airserver/Reflector or an AppleTV.
In order to connect your device via AirPlay to an external display you need special software or hardware.
You can use Airserver, Reflector or an AppleTV.
If you meet those requirements you now have to open the control center (on new devices by dragging down from the top right corner of the screen) and then press on "screen-mirroring" (not the music/audio area!). After that simply select the device you want to connect to.
Yes. This is now possible with iPadOS 13.4 and shiftscreen version 2.1.1.
In order to use shiftscreen in split-view, you always have to place the app on the left side of the iPad screen. Only the app on the left side can control the external display.
This way you can also open two apps (like shiftscreen and Goodnotes) in split-view and switch positions to switch what you see on the external display.
iOS (Safari) renders YouTube videos on top of the actual website itself. When broadcasting the selected window to the monitor the device only captures the website but not the video. Therefore the monitor shows a black or white box. For YouTube I have built a special player to control the video from the iPad or iPhone.
For other websites do the following: after you pressed play on a video, switch to "scrollpad-mode" or select another window to be active.
This page will be updated when new questions come up. If you need additional support contact me via the support page.