No. 6 is Rzewski's 5th Ballade "It Makes a Long Time Man Feel Bad".
In all fairness, for No. 2, you picked what is probably the codetta from the exposition (or possibly the recapitulation) of a sonata, which doesn't always contain anything related to the themes within the exposition, so there isn't really anything defining in said section, making it very difficult to guess what it is from, given that many codettas are very similar. My guess is that it is something by Mozart. Now, to go through the sheetmusic...