Yes but players are usually presented by their rank, e.g: Ke Jie 9P, Lee Sedol 9P.
Then, professional dans in some Go associations are granted by total wins over their career rather than relative strength to another rank (e.g: Japan).
There is already a wide range of strength among 9p players. In addition, once a player reaches 9p, they never lose it, so it includes players in their prime as well as players who have declined.
Yes, the ranking system you refer to is the one based on total wins over a player career and doesn't consider loses like ELO or other rating systems do.
Fernando Aguilar, a 6 dan amateur from Argentina (http://senseis.xmp.net/?FernandoAguilar) defeated 2 Nihon Kiin 9 professional dans (Hasegawa Sunao and Yo Kagen), which is unexpected given the substantial rank difference.
1) The two 9p professionals you mentioned achieved 9p status before the new promotion system you linked to. The new standards are much more stringent (though still based on lifetime achievement).
2) The standards differ by country. All the major countries now give out 9p ranks sparingly, but I think China especially may be quite difficult.
My understanding is that it was based on Oteai performance: there was an annual tournament and you had to score well enough against players of roughly your strength during a single year to improve. Winning half your games for 5 years in a row would not result in a promotion. Whereas today, you can grind out the requisite number of wins over the course of 2 years, 5 years or 10 years.
As such, the old system was, roughly speaking, based on your historical performance, not just wins.
But the bigger point is that it was very permissive. There were something like 70 9p professionals in Japan, and there will be quite fewer in the coming years (I believe Iyama Yuta is the only 9p aged less than 30).
Then, professional dans in some Go associations are granted by total wins over their career rather than relative strength to another rank (e.g: Japan).