2) Because Gmail's main economic contribution to Google isn't the advertising, it is in signing people up for Google accounts, just like Yahoo Mail's main purpose is to stickily draw people to the Yahoo front page. After you're logged in on Google, your rate of searching goes up, compared to otherwise demographically similar people who are not logged in. (Same if you use Chrome or the Google toolbar, by the way.) Google likes when you search because Google is a multinational advertising company and about two thirds of their inventory by revenues is on their own search result pages.

3) Separately from the totally rational reasons to prefer Gmail (a strategically important service with negligible marginal costs) over Picasa (a strategically marginal service with relatively high marginal costs), Google is also a big multinational corporation, and internal politics still happen there. There is a political angle to any project getting additional resources. Picasa is not politically favored compared to, I don't know, that I-can't-believe-its-not-Facebook that they launched recently.