Firstly, the Contractor should show the effects of the compensation event and show its effects (if any) on the “planned Completion” milestone. If this effect is agreed, the amount that planned Completion has moved by will allow Completion Date to be moved by the same amount. This is why the contract calls for a separate planned Completion and Completion Date milestones to be able to reflect this. Total float is shared by both Parties so if this compensation event does not move planned Completion whilst there may be some direct costs to consider there will be no time effect and no associated prelims to be included.
No compensation event directly moves Completion date. A compensation event only ever moves planned Completion, and if it does then you would move Completion Date by the same amount that planned Completion moved by due to the effects of the compensation event.
The Contractor can only claim for additional hire costs for equipment that they will now incur. If the equipment was due to be on site anyway and does not need to be on site longer then there is no additional cost that should be recovered as part of the CE. Labour costs they will incur even if the overall planned Completion is not moving would obviously be recoverable.
The intent of a compensation event is to put them in a position where they are no worse off but no better off after the assessment of a CE than they were before the CE.