Sounds like a Calliope
or some sort of Portative Organ
. (audio clip here
But I also wouldn't be surprised if they used an Ondes Martenot
One of the most intriguing and expressive synth-type instruments ever created.
Good Wikipedia article here
Very nice discussion on how it works and demo here
And another (in French) here
Tons more O-M videos on YouTube if you do a search.
Can't help you out with what the song being played is. It could be just about anything.
If it was done by a professional organist, it might not even be a specific song since these musicians are trained to be able to improvise. Unlike piano music, there are many formal organ pieces that have improvisational sections where the composer will leave some empty space and expect the performer to show off a little of his or her own virtuosity.
So what you're hearing might just be a segment of free form soloing (or noodling
) that was selected as the theme because the show's producers took a shine to it.