If you want to see excellent use of Baroque, check this video out.
Simultaneous supers you need to press the partner button right after you execute a super but I can't quite time it, I just find it easier pressing P (partner) at the same time so eg. with Ryu you would do QCF + ABP.
Yami is pretty simple, just chip damage him with basic A > B > C and burst if you get caught in his grab supers. Only trouble I had defeating Yami was with Gold Lightan because of his slow block.
I too am currently playing through No More Heroes, been on and off it for these past few weeks. I'm fifth rank at the moment. I love the presentation and feel but really hate the over world, breaks up the flow of the game I reckon, hope they ditch it in the sequel or make it a bit more lively.