Can you get statistical data on research paper submissions and publications?
IMHO, this is unlikely to fly. Some journals might give you statistics on the number of submitted and accepted publications. But submission to a journal is typically confidential and as an author, I would be pretty upset if Nature revealed this information to someone else.

Where you might be able to do similar analysis is a site like arXiv.org. It's used heavily in physics in other fields as a preprint service, and there are usually notes where and when a submission is accepted to a journal. Keywords are also included. The difference is that not everyone submitting to Phys Rev necessarily uses arXiv.org.