Phd Engineering admissions (2nd)

<p>Hello everyone! Had a few questions about my grad school application:
1-About research experience, does it help if i have a publication like the 'application of non-technical courses in engineering studies- a case study'? Or is it a complete waste of my time?
2- Also how much do ECAs such as Volleyball team captain and Spanish Club Vice-President add to my resume?
3- Which of these are more important to grad schools like Princeton and MIT?: Publications at the expense of internships or vice versa?
4- What are my chances if I have one publication a GPA from a relatively unknown int. uni of 3.97 and GREs (Q,V,W)=(770,550,4.5) but have a lot of volunteering and ECAs on my plate, along with 1 internship and a very strong LOR? i will apply hopefully next year to MIT and Princeton for ChemE.
And finally to those students who have been accepted to a PhD program? How many publications do most students have on average?
(Because from what I've read from these forums to get into the top schools you need 3 publications even with a 4.0)</p>