Adagio in G minor was actually composed by Remo Giazotto based on Albinoni's Sonata in G minor. A fragment of the Sonata was found amidst the ruins of the Saxon State Library, Dresden, bombed by the Allies in World War II. While the piece was not actually written by Albinoni, it is commonly attributed to him.
It was played as a short jam before Time Is Running Out on the earlier half of the 2006 tour. This arrangement featured Bellamy's Kaoss Pad, with Wolstenholme playing single notes on bass, and no percussion. This made its return when Bellamy got his doubleneck Manson guitar. Currently, he plays this as in the intro to Resistance with the top neck. He can be seen doing so in the footage of Resistance at Glastonbury 2010.
The piece is transposed to A minor, the key of Resistance, for live performances.
Adagio sostenuto means 'Sustained & At Ease' and is the tempo and name of many classical pieces, not just Rachmaninov's Piano Concerto No. 2. The piece played at the Seattle gig is indeed the piece played at the end of Neutron Star Collision, but is not taken from Rachmaninov's Piano Concerto No. 2. It is only similar in it's tempo and pace. The piece is pretty much written by Matthew Bellamy.
Originally a military march composed in 1897 by the Czech composer Julius Fučík, and later rearranged for a smaller band in 1910 by Canadian composer Louis-Phillipe Laurendeau. It was played during a few gigs between 2002 and 2007.