your questions:
1/2) Most of my projects have been 4-8 weeks. OK to get recommendations from someone who has only managed me for that long/ Is there any strategy to get recommendation letter writers to include this high praise in the recommendations?
As long as someone was supervising you, it's fine to get reco from short term assignments, just know that they may not be able to go into the kind of depth of analysis which could se you apart. Since they are very positive in their comments about you in reviews, perhaps you can simply encourage them to recall the review when it comes time for them to do the reco. Staying in touch with them is a good idea so they will not forget about your performance.2)
3) Will it have high impact, given most recommendations are probably strongly positive anyway. Any way to set myself apart?
Actually standing out for you will be a challenge, since your profile will be pretty common--good academics, good recos, good GMAT score. You likely know that in your applicant pool, the average GMAT is closer to 740 for the schools you are applying to, so you won't be a standout from a GMAT perspective. Ask yourself how you think you stand out against someone who has a similar background and you will be thinking about this the right way. As for your recommenders, the more specific they can be the better, so help them recall anecdotes where you outshone your colleagues. These kind of examples can help the adcoms put your performance in perspective.
4) Anything else I can do to show my strong performance (mention consistently high review scores, %ile etc.?) Where? It's really up to your recommenders to sing your praises on the job. If you do so yourself, you risk not sounding humble. Of course on your resume, you will list promotions or awards in the workplace, but just saying "I am awesome on the job and better than my colleagues is not a road you want to go down.
5) What are my general chances (profile below) - targeting HBS (top choice), Stanford GSB, Wharton
Again, you will face the same challenges all the other thousands of well qualified applicants will face, so your "general chances" are simply at or slightly worse than the posted acceptance rate. Why slightly worse? Because of your nationality and the competitive nature of that pool.
6) Company does not officially sponsor until after acceptance, but I have been verbally told I will be sponsored. Where can I show this? If you think it helps your case, you can mention it in your essays, but don't count on that helping you much. Certainly if there is a concern about financing the degree, and you have a bonafide sponsor to pay the way, it could in theory help, but more so for corporate or executive MBA programs, and your target schools don't have much to offer in that arena.