All pieces can move in all 3 dimensions. They can move up or down as easily as moving forwards. HexiChess has many parallels to traditional chess. Try promoting a single pawn. If you wish to use these pieces then you must ask me first.
Bishops move in such a way that they always stay on the same colour.
They move along the lines between hexagons. They can change layers the same way. They can only take pieces by moving forwards and to another layer, and they can only change layers to take. On reaching the other end they can be promoted. Never ignore the pawns.