How can I transfer a playlist straight to my PC?
There is no straightfoward solution as far as I know, but I solved this with the help of 2 free apps (with Android 4.1.2 on a Samsung S3 mini):


Total Commander
Playlist Backup


Install them from the Google Playstore, then continue as follows:


With Playlist Backup, export the Playlist as text file. Store it in a temp folder on your mobile.
To copy the MP3 files contained in the playlist, open the playlist in Android's built in player, then select "Send via" in the context menu. Select all files. Then, a list of apps is shown. Select Total Commander. In Total Commander, pick the local temporary folder (on your mobile) to copy the files into.
After Total Commander has copied the files, connect the mobile with your PC and copy the temporary folder to the PCs harddisk (containing the playlist text file and the MP3 files)


Finally edit the playlist file to adapt the paths in it so the MP3files are found by the PC player software (e.g. WinAmp or any other MP3 player which supports playlists).