I have been reading your article on repairing/removing shared chimney stacks on your website which has been very helpful. You mention that a Party Wall Notice is not required when removing a chimney, but is required for the remedial work when removing part of the shared chimney. Is a Party Wall Notice required when rebuilding the head of a chimney, and repairing the mid feathers? (There are a few courses in the mid feather missing, and some remaining bricks overhanging.)
The same principle applies to both parts of your question – the repair works are only be notifiable under the Act if they affect the wall dividing your flues from your neighbour’s flues. If you wanted to rebuild the whole of the head that could only be done in agreement with your neighbour. Looking at the condition of the head of the stack, re-building it jointly with your neighbour would be the best option.