Take a look at that Harvard MBA webpage again. It shows the industries (which is very diverse). I suggest you choose an industry that you like.
Notice that 40% of MBA students at Harvard are STEM majors. The number one correlation of success in an MBA program is mathematical skill.
Because they want the challenge, and also to be around other extremely intelligent people.
Yes. It holds, given similar GPA and performance in other entrance requirements.
Because: a) their family can afford it and wants them to attend, or b) as Harvard claims, 90% of American families will pay about the same cost to attend Harvard as their state school.
https://college.harvard.edu/financial-aid/how-aid-works/cost-attendance
Many elite schools guarantee to meet 100% of demonstrated need (often without loans).