Right, division directors and POCs probably aren't involved in the specific projects you are applying to. Division directors are managers that oversee a division, so they know who does what and where. And internship POCs are essentially managers who are matching up students with mentors. So while both aren't very technical, they both are a way to get connected to the mentor you are trying to get in touch with.
Search engines, social media, and offline networking are ways to find the names of the mentors. There is no best way since that can vary. Some mentors have web articles dedicated to them with their contact info. Other mentors like to boast about their projects on social media, but have no 3rd party news coverage.
Mentors can change from year to year. For instance, some mentors give it a try and decide they don't want to mentor a student next year. Sometimes there are multiple employees working on the same project, and their manager will want a different employee to get experience mentoring an intern. So while the project is the same, the mentor has changed.
With respect of what to say to program coordinators when you talk to them, well say what is it that you want and what you have to offer. They are very busy people so get to the point.
For me it would be: tell them who I am, how I found them, what I want, what I have to offer, and what they can do to help.
For instance, something along the lines of, I am a X year student at Y school, I was referred to you through Z website, I am interested in working in XY project, I have skills that can contribute to that project, attach resume, could you help put me in touch with the mentor for XY project?
Remember that the POC will not be the one to choose you for the job, so it is no use asking them for one. The mentor is the one who can decide because they have the technical knowledge to know, from your interview and resume, if you are fit for the job.
Hope this helps and let me know if you have more questions.