User Manual Denon AVRS750HBKE3 Receiver, 7.2 Channel (165W x 7) - 4K Ultra HD Home Theater (2019)

If they are Bluetooth wireless compatible then yes it will work

Not sure if I understand the question. However, my experience is that
airplay audio will be directed to all of the active zones as directed by
the receiver and the amps directing the sound to the various speaker
zones.

Have you checked with tech support? Or perhaps a community forum?
You can post this question on a forum. But it sounds like something's
broken because you shouldn't be losing sound when you change TV
channels.

I only use HDMI to connect to my TV for video and audio so I don't
have this issue.

You’ll have to make sure the input sound signal is surround (Like a
5.1) and not just a stereo signal (two channel). Try testing it out
with a DVD or Blu-Ray, or even a streaming service that has the 5.1
like Netflix. You’ve already verified that they are all working with the
test setup so the input signal is my best guess.