In my opinion these are all very good universities. They are all definitely reputable and will provide a strong education. I was already pretty sure but just checked and Michigan State University is ABET accredited for many forms of engineering. I do not think that small differences in ranking matter, even if “small” means let’s say the difference between #30 and #60. There are a lot of good engineering programs in the US (and not a lot of secrets that they are going to teach an undergraduate student).
I might add that I am assuming that we are talking about Penn State, Virginia Tech, and Michigan State (and that UIUC and TAMU are unambiguous).
Internships do matter. If a student does well in their classes then in some cases this might help the student to find internships. Getting to know your professors can also help (particularly if the professor finds that you are intelligent, a good student, responsible, and a reasonable person to deal with).
Of course engineering is not easy anywhere. IMHO this is a good thing since we need to trust the people who design a lot of things that we use every day.
For any international student, I would not count on being able to stay in the US after graduation. There is politics involved. Politics is not always completely rational in the US, but I suspect that this is true elsewhere as well. There is currently an option for students to work in the US for a short while after graduation (I think for one or two years?) which can provide some useful experience before returning to a home country.