Maybe there is a chimney builder in the forum who can say whether an installation shaft directly next to the chimney shaft is feasible :D
By the way, regarding the chimney at the eaves:
[*]for a roof pitch over 20%: the chimney outlet is at least 40 cm above the ridge or at least 230 cm away from the roof surface in horizontal distance. The same distance applies to exterior chimneys on the building's outer wall.
So it should be feasible according to regulations, as far as I understand. By the way, it is supposed to be a hip roof