Can the Employer use the site for works after the Completion Date but before the Contractor has achieved Completion without triggering a compensation event?
35.2 states that he can, yet this is take over of that part of the works and is a compensation event under 60.1 (15). However 60.1 (15) states that this is only relevant if the take over is before BOTH Completion and the Completion Date - the latter has passed.
Would this be a CE under 60.1 (5) and would the only factor be that the Employers intentions being mentioned in the WI?
It could be a compensation event under 60.1 (5), but the circumstances would have to much the bullet points in in 60.1 (5). There is not enough detail in your question to answer this, but use of the word “work” in all three bullet points implies they are doing something to the works, rather than using it.
To ‘use the site for works’ the Employer would need to take over that part or the Employer could be preventing the Contractor from accessing the Site, so possibly a CE under 60.1 (2). As you say it is not a compensation event as it doesn’t comply with Completion and Completion Date. A problem may arise where the part taken over is not complete and how this is dealt with under the contract. If it is taken over then there is an assumption that the Employer can use the works but that may not actually be the case. Maybe a further discussion topic.