I can't speak to chemical engineers specifically although it's my understanding that it's mostly civil engineers (and other engineers who work directly with regulators) who get PEs. I can tell you that as someone with mechanical engineering and material science degrees, it's not at all common for people in those fields to get PEs.

Continuing education is a bit of a joke. So you attend a conference once a year, maybe watch some webinars. In general, PEs mean you've gotten an undergrad degree, passed a couple of GRE-type tests and have worked in the industry for a few years.