Fyberskin is a specially-designed plastic banjo head with many of the characteristics of calfskin heads. That is, it's not so ice-pick-in-the-ears shrill or sharp as regular heads, and gives the plunkier sound that old-time banjo players seek. It doesn't react to humdiditty the way a real skin head does, though, which is why people developed 'em in the first place.
And "Mountains of Mourne" is the form of the parody used herein, but "Bendemeer's Stream" is the tune, and a very good tune it is. One of my favorites (see favorite tune thread). One of these days I'll get off my duff and look up the lyrics to "Bendemeer's Stream" and see if it matches the tune for singability.
Tenor banjos, as played in modern Irish settings, is actually a poor choice, since the tuning makes tune playing harder. The better choice would be a plectrum banjo, but they're rare birds and not often found.