I love the foam core stuff. You can get it really cheap from sign makers they use it for bilboardings at exhibitions etc so it generally gets chucked out after and off cuts are offten found waiting for the Trashmen. I use Good old Tamiya thick styrene glue and Revell Contacta, the one in the handy blue presision aplicator bottle thing that always get blocked up Other than that I use Zap A Gap Ca+ in its various guises. It glues most things including body parts.
generally its good for structural stuff and where you need to put putty o filler ontop, you can scribe it with pannelines if your careful, but its much better as a base material. I used it on my now on hold 1/55 custom.