If you are willing to spend a few bucks on a program I would suggest Pocket player. Aside from the most common formats this also plays .wma files as well as .m4a (itunes) files so that is why i use it primarily. I don't use play lists so I am not sure about your first requirement but as for the second requirement it continues to play without any problems. It still plays when the screen turns off as well as does play videos as well. Highly suggested. It does, however, cost $19.95 but I would definitely recommend it as a great media player for winmo phones.
http://www.conduits.com/products/player/
(no not a spokes person just one who thoroughly enjoys and uses this program a lot)