In order to fix the problems, navigate to Start, open Control Panel, press Uninstall a program and click the Turn Windows features on or off. Expand the Media Features list, uncheck the box next to Windows Media Player, click OK and reboot your computer. After that, enable again the player using the same procedure and launch it. In order to create a playlist, you need to press the Ctrl + N key combination and to type a name in the provided field:
Alternatively, press the Alt key from your keyboard and select Create Playlist from the File menu:
The playlist will be automatically saved in Windows Media Player library, and you will be able to add songs by drag and drop or if you right-click the file and select Add to > Your Playlist Name:
If you still can't create a playlist, I recommend you update Windows Media Player to the latest version.