Answers:
1. can a king take by co-ordinating with the co-ordinator, or does it
have to be after the co-ordinator's moves?
No, King only captures by replacement. Co-ordinate capture is performed by
the Coordinator, or by a Chameleon to capture an enemy Coordinator. King
can´t do that.
2. i assume that a king cannot move into check, and you have to tell
your
opponent if they do? i was playing against the applet linked off this
page, and you have to actually capture the king rather than checkmate it.
which is it?
Oficially, you can´t move into check. The object of the game is checkmate
the enemy King. Zillions implementation adopts the 'capture-the-King'
rule for technical reasons, the main reason is because if you immobilize
the King and you use the checkmate rule, it is interpreted by Zillions as
a Check, and it is not.
3. if white's co-ordinator is on f1, white's king on b1, and black's
king
moves onto say b7 from the c file... if the white co-ordinator has a
clear run to f7, is black's move therefore illegal?
Yes, this move is illegal, you are moving into check.