You should be able to clear the SDC updating issue by doing the following:

Go to "Tools > Settings" in SDC, you can select "Check for Stardock Central Release updates on startup" and "Prompt before updating Stardock Central" - then click "OK".

This will prevent SDC from attempting to install updates automatically, and will prompt you when a new official "Release" version is available.

As far as the downloading skins goes,

Can you right-click the skin you want to download, and then select "Save Target as.." > select "All Files" from the "Save as type:" drop-down list in Save dialog > save to your computer?

This will bypass the Stardock download manager, and should inidicate whether there is something going on in the program, or your internet connection. A successful download would mean that a setting in the program is suspect, or you have a download in queue, which is creating an issue.

You can also try verifying in "Tools > Settings > Advanced", that the download location is to: "C:\Documents and Settings\USERNAME\Local Settings\Temp\SDCentral".

You might also try going into "Tools > Settings > Internet > click the Internet Settings button > clear the "Resume partially downloaded files" > and then go to "C:\Documents and Settings\USERNAME\Local Settings\Temp\SDCentral" folder, and delete any folders that bear the name of the skins you were trying to download.

After that, try downloading again using the normal procedure in "SDC\Skins and Themes".

Note - these are just suggestions, as I have yet to see a consistent fix for this issue, which seems to pop-up every so often.