Music player for Linux which remembers the playback position
SMPlayer seems to meet most or all of your requirements (and more).
SMPlayer - Free Media Player for Windows and Linux with Youtube support - Official Site http://smplayer.sourceforge.net/
- supports multiple playlists YES
- remembers the playback position(file and time) for each playlist YES
- preferably, remembers playback position even when the process is killed NOT SURE
- lets the user adjust playback speed, without changing the pitch YES
Since I couldn't find such a player, I implemented one for my own use as a Python script, which supports playing .m3u files, and calls mplayer with the proper -ss value to resume playback where it left off last time. Get it from http://raw.github.com/pts/mplaylist/master/mplaylist (project page: http://github.com/pts/mplaylist).