Can I delete a SkyDrive folder from my computer but not from SkyDrive cloud storage?
This can be done. Skydrive has a new feature called Smart Files, which allows you to selectively sync.
Open your Skydrive folder, in the Desktop, not Metro, select the Details view, and note the column 'Availability'. This tells you whether the files are on your computer ('Available offline') or in Skydrive only ('Online-only').
You can right-click on a file or folder and there's a context-sensitive menu entry to change the online status. In your case you'd want to select 'Make available online-only'.
There's an introduction to the feature here: Skydrive Introduces Smart Files
and a more detailed description of the process I'm describing here (it's the first answer, by 'Vasudev'): 'How can I delete folders from my HDD without deleting them in Skydrive'
Update: There's also a way to do this from the Metro ("Modern") Skydrive app. Open it, make sure you have Skydrive selected in the top-left corner. Right-click or press and hold to select a file or folder, and you'll see in the middle of the app bar which appears at the bottom of the screen, a button for Make offline/online. Details and screenshots here: Deeper Skydrive Integration in Windows 8.1