This is almost too easy for Powershell that it is almost not worth it to learn. 😉 But if you like to do it anyway (and I would definitely recommend it) you can find some great starting points in this post: Beginner Sites and Tutorials.
Because it is so straight forward you need in this case the same amount of cmdlets you would need in batch commands – 2.
Remove-Item -Path 'Path to your directory containing the subfolders to delete with a following "\*"' -Recurse -Force
... and to remove a shortcut from the desktop ... take a guess ...
Remove-Item -Path 'complete path to your shortcut file including the extension'