Other answers.
1> You will not be limited to grad schools with any of these as an undergrad
2> Undergrads doing research happen just about everywhere and at Purdue I think it is even required with honors college to do some sort of research. Big Research Universities always seem to prioritize graduate research, but it isn’t a binary situation.
3> UChicago does have engineering, albeit not in the sense that it is Aero or IE. But, they do have Molecular Engineering.
4> ABET is over rated and I know of nobody in industry who will shy away from a UChicago undergrad in molecular engineering because it isn’t ABET certified.
5> CMU is a great school. I do think you’ll have more opportunities to “play engineer” at bigger engineering schools in terms of clubs and orgs.
6> I for one wouldn’t go to a school not knowing if I’d get into engineering school. At Purdue, at least you are pretty much guaranteed an engineering school, you won’t have an issue getting into IE, it isn’t one of the super coveted majors. And, if you are good enough to get into the honors college, you should have little problem getting into AE if you make studying a priority.
7> Which school has better grading policies? Here is a bit of advice I’ll give that I learned the hard way. When I was getting my MS in IE at Purdue, I worked my tail off the first semester and got my first 4.0 of my college career. I felt very accomplished. I then found out others in my class who didn’t work nearly as hard or do, in my opinion, nearly as good of work. I was pretty upset. Upset enough to talk to my advisor about it. She told me my motivations are wrong. I should try to learn as much as I can about the topic and the grades will take care of themselves. From that point on, through the remainder of that degree and then my MBA, my grades took care of themselves. It was some advice that I wished someone would have told me sooner. You go to school to learn, not to get a grade. You sound like you are very bright, I don’t think you’ll have a problem being successful anywhere. Especially if you are going to learn, not get a grade.