If you need to "extract" an image from a Pages document, add extension .zip to the filename, double-click it and grab the image from the unzipped folder structure. More comfortable are tools like StuffitDeluxe's Archive Manager, that can browse the document contents directly (Maybe The Archive Browser from Unarchiver site can do this, too).
For the initial question on how to split any file format and output any file format, maybe GraphicConverter by Lemke Software is the best answer. It has a Split function and can read and write a lot of file formats. Though, I think there are plenty of alternatives that can be used for this task, if one narrows down file formats. If Preview works, then just use it.