Does anyone know if it is possible to sync, or import, your Skype message history from:
1. Skype For Desktop to Skype For Windows 8 on the same PC.
2. Skype For Desktop on a PC to Skype For Desktop on a Laptop/Notebook.
For example, if you sync the C:\Users\(UserName)\AppData\Roaming\Skype\(SkypeName) folder on the PC and the Laptop, will that do it?
Can it be done via SkyDrive?
Where does Skype For Windows 8 keep its data files?
Any ideas would be appreciated.

Skype history remains same when ever you log-in to different computers using same id. you need not back-up or sync the Skype history if you are using same id on different computers. If you are using different id and you want to back-up the data, Try the following steps.

Type %APPDATA%\Skype in RUN to open Skype’s Appdata folder, there you will able to see the folders in the name of usernames used to login in that local system. Make sure you have exit the Skype application from tray or you can choose to sign out. Then just copy the folder with your username to your desired location for backup.

Steps:
1. Press Windows + R > %APPDATA%\Skype
2. find the folder which is same as your username.
3. copy and paste it in your backup location.
You can use the same folder in another computer to have the chat history there in another computer.

If you are using any cloud file sync service (like Dropbox, SkyDrive, Google Drive, etc.) between different computers, you may use that to sync that between different computers and backup as well.

In case you are concerned about security about using Skype in shared computer, you can delete your Skype username folder to erase all trace you have had in that computer related to Skype.