What is the distinction between the WAN Ethernet and plain jane Ethernet ports? I understand their function in router mode. But what about bridge mode--am I correct in thinking it doesn't (or shouldn't) make a difference whether I use the WAN or other Ethernet ports in bridge mode?
In bridge mode wan port is assigned to LAN.. there is no WAN port as correctly you have figured out there is no router.
However please do not use WAN port in the new AC model AE as they are unreliable.. it is better to use LAN.. if at all possible leave the WAN port unused.
What exactly does roaming do? Does this mean AEs work together to determine which AE can provide the best signal to a client and drop weak(er)-signal clients as needed to encourage clients to reconnect to a better signal? The more detail, the better; it-just-works answers needn't apply.
Just the same as your mobile phone.. when you drive along it swaps tower to tower as signal from one goes less and signal from the next one grows stronger.. at some point there is a swap over.. that is how they track your position on a mobile phone without GPS. People can trace your movements from which towers your phone linked to.
WiFi technology uses the same idea.. although sadly it is much less able.. so in theory as you walk around the device should swap "towers" (ie AP's in the house).. in reality some stuff works.. and some doesn't.. the stupid thing is the stuff that does not work is often your iOS stuff which should as it is more mobile.. and your laptop will roam just fine and you are probably not even carrying it around.
In other words.. this is voodoo technology still.. be aware you might need to kick it (figuratively at least) by turning off wireless and then on again.. to enforce the change of towers.
For roaming, must AEs be connected as below?
Either of your configurations will work.. they amount to the same thing.
router (NAT,DHCP)------->(switch)------>AE (bridge)
| \
| \
| \
| \
AE (bridge) AE (bridge) ...
This is the right way.. In terms of network maintenance this is hugely easier to track what is going on.
Daisy chain also works.. but it is dependent on every step working for the last one to work.
One important rule btw.. In both your diagrams.. you have correctly shown the network does not loop back on itself.. this is important.. you can daisy chain almost unlimited numbers of switches these days.. there used to be limits.. but you must never connect the last item back to the first.
If AEs must be daisy-chained for roaming, does it matter which Ethernet ports are connected between the daisy-chained units? Any additional configuration required for roaming to work?
You do not have to daisy chain. If you do daisy chain there is no problem with the ports.. except as noted above try and avoid using the WAN in the latest AE or TC models.. it is unreliable. LAN to LAN nowadays all works automagically to determine sender and receiver.
The important thing in roaming is same name (ssid) on every unit.. same password and security settings.. different channels.. that is a problem because there are limited channels.. and sometimes I find the apple routers do not work as efficiently as they should.. the bigger the roaming network the more important it is to set static wireless channels as best as you can to keep interference low.
(How) do high-density deployments (multiple AEs with overlapping range) affect roaming?
Do not use AE for business networks.. they are home devices.. using 2 or 3 is fine.. after that expect issues.. however as pointed out above taking control and using the network as best as you can at network setup stage will reduce issues later.
For big deployments get pro gear and pro installer. Apple routers might be neat and easy but they have zero management.. pro gear will allow a lot more control.. and management which is vital for network where large wireless arrays are used.