Can I record a Keynote presentation with live video and use my iPhone as a laser pointer?

Keynote is unable to record the laser pointer effect from Keynote Remote.

You would need to use a screen recording application to record the Keynote laser pointer and the existing sound recording. You would play back the recorded slideshow and record the screen while using the laser pointer. There's Capto, from the Mac App Store at only £10.00. There is a free trial here: https://www.globaldelight.com/capto/

Live Video

Either use the builtin camera or use a compatible external camera

You can show one camera or both on a slide

1 - Go to: Insert > Live Video

2 - To record the slideshow, go to Play > Record Slideshow

see Apples webpage here: Record Keynote presentations on Mac – Apple Support (UK)

3 - To use iPhone to annotate the slides, go to Apples webpage for full details:

Use Keynote Remote to control your Keynote presentation – Apple Support (UK)