I presume the BT router is distributing IP addresses to my network?
That is correct.
if I give the Airport's static address in their configuration, do I need to restart my entire network so there aren't conflicts, etc ?
That would be a good idea. It may not be absolutely necessary, but I would do this if possible.
Or do I just set them up as static with the ones the currently have (so clearly not used) and good to go?
This all depends on whether you want to set up "Static" on the AirPorts using AirPort Utility, in which case, the "Static" IP address will be the same IP address that is currently assigned to the AirPort.......or.......whether you want to set up dedicated Static IP addresses on your BT router, assuming it has that capability, which it should. These settings might be under an Advanced Option or something like that on the BT Router, so you'll need to be able to get into the settings on the BT router to make changes. BT Support may or may not be willing to help you with this.
the router will know not to assign these to anything new in the future and to the extent devices join / restart they will not use something already using a static address?
That is correct. If you decide assign Static IP addresses from the BT router, it would also be a good idea to assign a Static IP address to your printer. That way, it will always get the same IP address.
Or do I need to reserve these somewhere in the BT router so that the IP addresses are not used by another device?
That is an option if you want to assign specific IP addresses to the AirPorts......like the example that I gave above where the AirPorts get 192.168.1.100, 192.168.1.101 and 192.168.1.102 addresses or similar. The advantage would be that it will be very easy to identify any of the AirPorts since they have easily recognized IP addresses.
That being said, it is not a strict requirement to use Static IP addresses at all, but it is a good idea to do so.
You both mentioned the network in "Off (Bridge mode)" - but what about the Wi-Fi network ? (which is in "Create a wireless network") Is that the correct settings for all 3, and should I always have channel settings as automatic/
Here is an important tip for you. If any AirPort connects to the network using an Ethernet connection, then the correct Wireless setting will always be "Create a wireless network". Golden Rule.
You would want to use the Automatic setting for Channel selection to allow each AirPort to scan among other WiFi networks in your area and then select the best channels available for each AirPort automatically.
I suppose that you could guess at trying to set a channel manually, but which channel to choose? Even if you guess well at a good channel to use, other WiFi routers in your area are automatically changing their channels to look for the best setting, so the "right" channel now may not be the best setting in a few hours.
You may find that the AirPorts are using different channels when you check or they might be using the same channels. I pay no attention to this at all.