1. Differences between Community Foundations / donor-advised funds and Private Foundations can be found here: http://www.programforgiving.org/charitable/pages/considering...
EDIT: of course, this only applies if the company issues a dividend
Let's say Mark plans on donating $500M to an organization and this month he also wants to buy $300M of Christmas presents. He only has about $600M lying around, but he has a lot of FB stock. He can donate $500M cash, then sell stock to have enough money to buy the presents but he'll pay capital gains. Or he can donate the stock, avoid taxes, and use his cash for the presents instead.
I would be shocked to find they sold the shares. I'm sure them keeping them for a long period of time (possibly forever) and Zuck retaining voting power over them was a key part of this transaction.