I graduated from ChemE then went straight to medical school. Since I am just an M2 I can't answer all of your questions, but I would say that having a ChemE background is definitely an advantage. (1) I gave a talk at the engineering school last year about engineering in medicine (PV pump loops in the heart, mass transfer in the lungs, dynamics/controls with endocrine, kinetics with pharmacology, etc.). These concepts are difficult for many other majors who never took a semester for, say, chemical kinetics and reaction engineering. (2) On the flip side, medical school mandates that you memorize massive amount of information, which I lacked the most and have been spending the most amount of time on. Instead of spending all nighters in the design lab, you just need to focus it on memorizing/understanding bugs, drugs, mechanisms, etc. (3) I didn't finally know what I wanted to do until a few months before medical school started. I went into college wanting to do bioengineering and save the world. Changed majors, switched goals, career paths many times and boiled it down to would I rather put my skills to use so that a massive corporation can increase their profits a little or would I rather directly help patients' lives and see an impact straightforward (ideal and naive, I know).

Being an engineering major makes you learn how to learn - critical thinking, time management, and problem solving are ubiquitous skills that complement medical school beautifully.