How to keep Skype open on multiple virtual desktops on Windows 10
I describe below how one can open as many Skype sessions as required, but the sessions must be opened with different accounts.
Start the first Skype session as usual, by using the Skype icon.
To launch a second Skype application, press Windows + R to open the Run dialog, copy-paste the below command into it, and press Enter.
For a 64-bit version of Windows :
"C:\Program Files (x86)\Skype\Phone\Skype.exe" /secondary
For a 32-bit version of Windows :
"C:\Program Files\Skype\Phone\Skype.exe" /secondary
You can repeat this process to open a third, fourth, and other additional copies of Skype. Sign into each Skype window with a new account.
There is currently no native support in Windows 10 to pin windows to multiple desktops. When the anniversary update comes around (I believe it's August 2nd), this will be possible. You could update to an insider preview build if you want it now. It's available from build 14316.
source
Since August 2nd 2016 (Windows 10 anniversary update) it is possible to show apps and their windows on all virtual desktops:
From the Windows blog:
You can now pin a window so it’s available on every desktop. To do this, launch Task View then right-click on the window you want to pin and choose “Show this window on all desktops”. Try pinning Skype or Groove Music so they’re always at your fingertips. And if you have a multi-mon setup, you might enjoy the ability to have your email app on the second monitor no matter which desktop you switch to.