VC and Business Analytics Extern Advice

I recently received a VC and BA remote externship at a large computer/tech company (Think HP, Dell, and/or Intel). My past two experiences have been in commercial banking and mortgages. I am currently an incoming sophomore in college and I go to a somewhat unknown state school.

I have a 3.90 GPA and am working on a double major in Corporate Finance and Honors Economics along with an Applied Statistics Minor. I also hold 2 lower level leadership positions in two finace based clubs/organizations at my school. Just to add this in hear, I have a small online business that has done extremely well for me and helps with the costs of college.

The three main areas of work that really have begun to interest me are PE/VC, IB, and Corporate Finance. My interest level in these three areas are in that order. 

I did not think it would be possible to work on wall street without going to a really good university until I received this highly sought after position. Just to frame my self out a bit more for everyone, I am not a minority, and I come from a middle class family. 

I have six main questions that I am looking for advice on.

Question 1: Would this externship create a siginificant advantage in getting into PE? From what I understand PE and VC are related.

Question 2: Considering my academic load, should I add Business Administration on as a third major? I have mapped out all of the course work, and it would be entirely possible to graduate in four years with a triple major and a minor. Without adding this in I would atleast graduate a semester early. I think this would be an easy third major that might make my resume look a little better. Any additional thoughts on this or maybe a different third major? How much of an advantage would this be?

Question 3: I also know a VP at one of the biggest banks in the world. They do not work in finance, but they work in another division if you will. I believe that if I spoke with him/her they would be willing to help me break into their bank. The question I have regarding this is how much does having this connection help me, and what could they do for me in the recruiting/application process all things considered?

Question 4: Considering that I go to an almost no name school but have all these other resume builders, what do you think are my prospects of working on wall street at some level?

Question 5: I have an externship, not an internship. From what I understand, I will be meeting with company managers and learning on the fly while I work on company projects. Does an externship look less than on a resume? If so, has this been less of a break through than I think it is?

Question 6: For most of my life I have worked for myself in some capacity. I have half the mind to nix working a job after college and work for myself. I have even pondered dropping out, but I am pretty certain I do not want to this. What do you think about this? Should I work for myself or work a job? Would I be making a huge mistake by working for myself and even starting another business? I think PE/VC/IB would be one of/the only kind of job that would satisfy my urge to work for myself like I always have.