International applicant for a Phd in the US

[curvilineardisparity]

I've been reading the forum for quite some time, but it is my first time posting here. I'm an international student currently preparing my application for a PhD in Political Science or Public Policy in the US and would really appreciate to hear your comments on how to improve my application (questions below).

Academia:
Undergrad: Economics, 5 years, mid-level Brazilian university, GPA~2.5, thesis on public budget in Brazil.
1st Master's degree: Public Administration (courses on PolSci, Law and Economics), 2 years, mid-level Brazilian university, GPA=4.0, thesis on innovation policy & economic growth in Latin America, with full scholarship.
2nd Master's degree: Public Economics, Law and Politics, 2 years, mid-level German university, GPA (by now)~3.0, thesis on political parties in Latin America, with full scholarship, plus assistantship at a Development Economics course at the BA level.
Lecturer: Economics, Marketing and Financial Maths, 2 semesters, mid-level Brazilian university.
Others: short-term courses (i.e. summer schools) in over 10 countries.
Publications: 
One paper in a Polish journal, two papers in Brazilian journals; oral presentations at international renowned congresses as Development Studies Association (Oxford U), International Political Science Association, European Association for Evolutionary Political Economy, and a graduate conference on political theory at SciencesPo.
Work experience:
National bureau positions in a Brazilian political party's youth wing for ~7 years; treasurer and program manager at an international NGO based in the UK for ~6 years; political consultant for different politicians in Brazil, incl. a former minister for ~8 years; part-time jobs in small-sized consulting firms in Germany as finance coordinator and market researcher (energy sector) for 6 months each.
Languages: Portuguese (native), Spanish (upper-intermediate), German (intermediate), English (TOEFL: 104, 3 years ago, I guess I have to retake it).
GRE: will take it in October. Very worried about it, as I feel myself very dumb when looking at the content.

"Dream" universities: MIT, Georgia Tech or George Mason (although I believe that with not-high scores on GRE and coming from mid-level unis would not allow me to be accepted).

Well, my questions are:
1) How much does coming from mid-level (not famous) international universities harm my application?
2) If I don't score high (or even in the 50th percentile) on GRE, would I still have chances with my CV?
3) In the case of low GRE scores, would you recommend any uni in the fields of either innovation or political parties in Latin America?
4) The applications are in December/January. I'm trying to improve my CV by having more publications. Is there any other thing I can do now?
5) On which aspects should I focus my application?
6) Do you believe the three listed universities would be a feasible target? Unfortunately my budget only allow me to apply for 3 universities, so I must be pretty assertive.
7) Should I approach potential supervisors before applying? If yes, how do you suggest doing so?
8) Any other suggestions or comments? I'd really appreciate hearing from you!


Thank you very much for all of you contributing to it!  

[Determinedandnervous]

Well, in terms of political science Georgia Tech does not have a PhD program in it. I think your GPA for certain programs may be low, but you more than make up for it in independent research experience. That being said, do as well as you can on the GRE. They frequently just pick a cutoff and throw out applications below it without reading.

For the public policy stuff, go to the Government Affairs subforum here (I think that's what it's called). It's in the professional programs category.

[curvilineardisparity]

28 minutes ago, Determinedandnervous said:

Well, in terms of political science Georgia Tech does not have a PhD program in it. I think your GPA for certain programs may be low, but you more than make up for it in independent research experience. That being said, do as well as you can on the GRE. They frequently just pick a cutoff and throw out applications below it without reading.

For the public policy stuff, go to the Government Affairs subforum here (I think that's what it's called). It's in the professional programs category.

Thanks for the answer, @Determinedandnervous!  

At Georgia Tech I'm planning to apply for the Public Policy program. I'll publish a post in the other forum about it. Thanks!
As of my GPA, that's a serious concern for me. Are there interesting programs where it would not be a problem? As a safe option, maybe.

[Determinedandnervous]

If you're applying to public policy schools, they care much less about your GPA. With political science programs it matters much more.