All Rook Endgames are Drawn (but it can take a miracle)

Seigbert Tarrrasch, one of the top players of the 19th century once claimed that all rook endgames are drawn. It was something of an exageration, but there is definitely a grain of truth. By getting active pieces the defending side can frequently hold positions down a pawn or two. I've decided to share one of my defensive efforts from the Washington International a couple of years ago, the strongest tournament I've ever participated in. The endgame is too complicated for me to make a 100% clear evaluation of some lines, so feel free to add any analysis of your own. 

First, a few puzzles.

 1. White to move and draw