The first is Colonel Catherine (Cady) Coleman, on the International Space Station, playing a duet with Ian Anderson, on Earth. They are playing a rendition of Bach's "Bouree," which Anderson had made a hit while he was with the group Jethro Tull.
That makes an interesting complement to this Star Trek scene from the episode "The Inner Light" (1992).
The second video I've only just seen. Canadian astronaut Commander Chris Hadfield sings a cover version of David Bowie's "Space Oddity" while up in space.
Background information on this performance is on Ars Technica.
To go with that performance, have a look at Andrew Kolb's take on the song. (The pdf is here). His illustrations turn Bowie's lyrics into a sad and moving children's book.