Welcome to the Ranch
You seemed to learn exam codes well. Un/Fortunately there is much more behind these. Glad to see your enthusiasm and a good mindset to get more knowledge.
Campbell is right. First and most important is your degree at the moment probably, for the rest tasks - how time permits.
I'd say put away thoughts about OCPJP (for the time being), that's almost certain. It must be fairly difficult exam, which requires much broader knowledge than OCAJP. Beware, OCAJP isn't easy too, but doable, taking in account that you also studying. Apparently there are students who want to learn programming not just during the classes time but also outside - that's exemplary.
Agh, nearly forgot your questions. No, there are no pre-conditions for being graduated in order to sit an exam. However, there is condition for OCPJP. You can sit OCPJP without sitting first OCAJP, but you get accredited with OCPJP only after you pass both exams (OCAJP and OCPJP). Once again, I'd recommend to start with OCAJP.
Good luck!