Hi there,
Thanks for posting and sharing all of the profile highlights you've listed.
You've got a lot going for you in your profile thus far, and I would feel you are well-positioned for consideration at top business schools.
Strengths:
-finance management and trading experience in the energy sector (will likely get noticed and be of interest)
-strong international experience
-great leadership and management experiences you could contribute to the class (such as leading the team of 50 as you mentioned etc)
-solid overall GMAT, strong academics
-goals make sense
-some community involvement and other activities
Potential weaknesses:
-GMAT quant score
-maybe could be stronger extracurricular activities but what you've listed is not bad, especially if you can talk in more detail about some of them
Unknowns:
-more detail on work experience, teamwork skills, etc
-essays/recommendations/interviews!
There's no real way to just list xyz skills that you "will get into", since the process involves holistic assessments of each candidate, often by multiple members of the admissions committee, and can be somewhat subjective... beyond GMAT and GPA, schools will look at your work experience, leadership & management potential, what you'll contribute to the class, how you'll use the MBA, why you want to go to their school, who you are as a person, etc.
All that said I'd believe that WITH a strong application, and essays!!, that you would potentially be considered at top b-schools including those you mentioned. Keep in mind that Stanford and HBS are of course extremely competitive... so sometimes it's not something you are lacking that keeps a strong candidate out, it's that another candidate was even MORE remarkable on various levels. And Stanford's class size is much smaller than many of the others so the statistical odds of acceptance there are even lower than other top schools. But generally you may be considered, and would have slightly better chances at the others you listed. LBS would likely value your international experience in Africa (though all schools would). As for the quant percentile, some specific programs may have an issue with that, such as Wharton... and a school like Haas may require an extra pre-MBA course. But beyond that it's tough to say... yes closer to 80th percentile would be preferable, but quant scores have been increasing more and more in recent years, and as you said, there is other evidence of quant ability which would help.
Keep us posted on additional questions, and your decisions! Good luck!