If the Contractor disagrees with the Project Manager’s action/response e.g. withholding payment or issues with X7 applied, how is this countered by the Contractor?
The “appeal” process in NEC3 for anything ultimately is adjudication. Before that you have the early warning process, where you can advise that withholding money that you don’t think is correct is potentially going to cause you problems in delivering the works they want you to deliver. That should lead to an action to benefit the project. You can also try to speak to senior management - which is actually now a formal dispute process within NEC4 that is undertaken before going to adjudication.
If talking fails then ultimately it would be adjudication. Withholding payment during the project is a tricky one though to take to adjudication, as the process can take up to 28 days which is when the next payment is due anyway and they may then have paid the money in the next period anyway. If they have charged delay damages that you think incorrect, then that is a case of looking at compensation event assessments as to whether they have been implemented at what the Contractor considers to be correct in terms of cost but more importantly time.
The only way the Contractor can be charged delay damages is if they have exceeded the Completion Date (or a sectional Completion Date), and the only way to get a Completion Date moved so that they are not liable is through an implemented compensation event. Therefore the dispute that could be taken to adjudication is whether the CE has been implemented correctly. If found to be incorrect and Completion Date should be moved then you will be paid the money back with interest (and the Employer picks up the adjudicators cost). Thankfully in my experience the threat of adjudication as the Contractor is adamant they are correct is normally enough to get the Parties back around the table and reach an agreement.