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’