What are the correct display settings for doing color correction in either FCPX and DR for MacBook Pro XDR P1600 displays?

I'm about to begin work on the color correction and color grading of my low budget documentary, I edited in FCPX. The footage was filmed using S-log 2 and HLG on a full frame 4K camera. I recently purchased an M3 MacBook Pro Max with a P3 1600 monitor to speed up the rendering and for the display. The documentary will be viewed on a 2K Rec 709 Christie theatrical projector. I'm doing the final color grade in Davinci and will export using its DCP feature.

Before I begin the color grade, there are a number of different options for my MacBook Pro XDR P3 1600 nits display, including one for theatrical projection. However, it's been recommended that I use the P3 1600 setting and use Apple and DR color management in the timeline workspace. For output, I'm using DR to assist for the cinema projector output conversion.

1. Am I on the right track color grading in P3 1600 setting?
2. Also, is my XDR P3 1600 display Rec 709 2.2, Rec 709 2.4, or something else? I need to know this for my timeline settings.
3. Finally, what is the correct Rec 709 output setting for a 2k Christie Rec 709 projector?

PS Yes, I know I should be working with a calibrated reference monitor.