How should Contractor go through to assess cost in a quotation for addition work?
Should they base their quote on any assumptions? What level of detail is required?
Contractor should produce the quotation in line with the schedule of cost components in enough detail that convinces the Project Manager that it is a fair quotation with a sensible amount of risk applied.
Contractor should not include their own assumptions within the quotation, they should instead price the risk of that item. The only contractual assumptions are Project Manager assumptions which if given are the only part of a quote that should be revisited. They could suggest some to the Project Manager during the quotation stage, but to be valid the PM would have to play these back to the Contractor (in writing) to make them PM assumptions under clause 61.6 which can then be revisited.
In my experience these should be used much more to help quotations become agreed in a more timely fashion making it clear which bits are the Contractor risk and which are not.