1. Dynamics
You're right, that would be very interesting. The most obvious way we could have done this is by looking at the spread of our app itself as people started to use it. Unfortunately, we only started recording anonymized stats for the second release, so we've somewhat missed the boat there.
To do it with links and general "memes" would be technically much harder, because we'd have to periodically rescrape walls of all the donors to see time evolution. It was somewhat out of scope of the blog post, given all the more basic stuff we could do instead.
I'd be surprised if Facebook didn't already do an analysis of this when they "cracked down" on app virality a while back.
Bit.ly's Hilary Mason might have looked at this question too, and I'm sure it has been done to death with Twitter, though the demograph info is much sparser there.
2. This not being a scientific paper, we estimated it by drawing on the log-log CDF. Barring the noise that "deparadoxing" the friend's friend count distribution induces on the low end of the distribution, it was very linear over two decades. We didn't think the exact number was all that interesting, so we didn't spend any more effort than that. Facebook's anatomy paper probably has a very accurate number.
I'd heard about the fictive power law stuff. What makes me even more skeptical is that FB friends are probably a poor proxy for 'true' friends. You'd be better off looking at number of friends as defined by some cross-commenting threshold.
3. Thanks! It was a lot of fun!