Sorry to hear you are having issues.
How can I exclusively enable skinning of windows only and leave everything else untouched, especially start menu and taskbar?
There is no option in that. For Windows 10, Start menu will not change if you don't have Start10 installed. Taskbar will always change follow the skin you use. You have an option to use different skin for your Startmenu and taskbar, but there is no option to totally set it to Default Windows 10 style.
I can't get the WindowBlinds tray icon to show in the Windows tray, even though I have enabled the option in the Settings. What can I do?
You mean this (refer screenshot below)? or something else?
Is it really the case that WindowBlinds skins are still not adapted to Retina/HiDPI screens? My 4K screens are running at 200% dpi, and the WindowBlinds window buttons etc. are all blurry.
It is best to restart Windows if you changing Windows scale for the GUI to show up properly.
Stardock Community Assistant.