When being accepted individually in a PhD program, one needs a certain amount of publication work to come up with along with their dissertaition. Are there any rules regarding the number of publications, papers or books created collectively by a research group? If some want-to-be researchers team up, how can they pursue their PhDs together?
This is not generally how it works. One does not "team up" and work on a PhD together in that sense. By definition, a PhD is a proof of an individual's capability to do research. Of course, many PhD students can collaborate a lot, and work on a joint project - but even in that case, each student needs his own research questions, his own papers, and, ultimately, his own thesis.
EDIT: just to clarify a bit more. Collaboration is entirely ok, but when PhD students work together, every research contribution (not necessarily each piece of e.g., code or data) needs to be mappable to exactly one student, and each student needs to have a few of those contributions that clearly were his part in the project. I have seen very bad collaborations, where, essentially, person A was churning out ideas and papers, and person B was writing all the code (because he liked programming). In a company, this model is perfectly fine, in a research context this is highly abusive towards person B.