There's no lower limit set to get into a top 10 business school. GMAT is but one component of your application and the schools are going to evaluate your candidature based on other certain other parameters. A high GMAT score is neither a necessary nor a sufficient condition to get admitted to a top 10 school.
Having said that, getting through the top 10 is an ultra competitive task and the average GMAT scores at the top 10 hover around 710, which can go as high as 730-the average GMAT score in the current batches at Stanford. Similarly at Harvard,the average is somewhere around 720,but the interesting thing is that the lowest GMAT score in the current class is a 540. I am sure that this 540 candidate would have had an exceptional profile or might have been the son/daughter of a corporate mogul.
You seem to have a pretty impressive profile and I think if you're able to sail past the 650 mark, you should be in a comfortable zone. However, higher, the better.

Regarding the time required to prepare for the GMAT,it depends from individual to individual . For me, it took around 2.5 months; some get fabulous scores by studying just for one month while some don't landup their desired scores even after preparing for more than 6 months. Broadly speaking, 100 days is supposed to be the ideal time to get a good GMAT score provided you have the right strategy from the beginning and you maintain discipline throughout your preparation.
Hope that helps!