Saez's contribution to economics was a novel way to measure income inequality of really small percentages (top 1%, 0.1% etc.) of the population.
That may be, but income statistics like the one cited here don't require anything novel: The IRS publishes everything you'd need to know.
No it doesn't, that's the point. The IRS publishes the top 1% and I believe the top 0.1%, but it does not cover the top 0.01% which you cited.
http://www.irs.gov/pub/irs-soi/08in12ms.xls
Try dividing the number of $10M+ earners by the total number of taxable returns. You'll get a number surprisingly close to .01%.
Yes, what Piketty and Saez did was a more sophisticated operation on IRS data to get a time series so that we can measure exactly how the top 0.01% etc. did.
Here's the link to the paper if you want the details. http://elsa.berkeley.edu/~saez/
By the way, if you took the data from the census and measured wealth instead of income, you would get a far more extreme differences in inequality. This makes sense of course, since wealthier people have more money in the stock market.
You are correct that the rich lost a lot during the stock market crash in 2008, but it similarly recovers quickly as the market rallied. Again, this is a natural effect of wealthier people having more money in the stock market.