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That's a lot of questions, Charles. However, I am very pleased to answer them, as I gladly learned from you - to my own surprise - that the pun of the hexagon leading to a witch's game does somehow work in the English language, too.
Well, the original German 'Hexenschach' names of the figures are Rabe, Hexe, Besen, Fledermaus, Turm and Kröte. You can find these names together with the German names of the conventional chess figures on the game's original webpage <a href='http://www.hexenspiel.de/'>www.hexenspiel.de</a>.
Concerning the two besoms I want to refer you to the FIDE chess rules, which explicitly state (see Article 2.2: 'At the beginning of the game ...') that each party has two bishops.
We wanted to make as few changes as possible to the FIDE rules, which do not raise the issue of whether the bishops cover the fields of all colours. Moreover, we did not want to have too many figures because early experiments with really large boards and many figures led to everlasting games. For reasons of symmetrie, we left the centre field uncovered.
However, to tell you the truth, that's not all. I mean, the proof of the Pudding is in the eating. Thus, I have just added on the <a href='http://www.hexenspiel.de/engl/witch/'>Chess Witch's Homepage</a> further information as to what happened to the third broom.