The ideal situation is to configure the Extreme as described above, and then to configure the Expresses by connecting their WAN ports to an available LAN port on the Extreme, and setting them up in Bridge Mode using DHCP. Correct?
The Express should be setup in bridge mode.. so on the Network tab it shows Off (bridge mode).. on the Internet tab it says dhcp. On the wireless tab you MUST create a wireless network.. not extend.. that is the key point.
So I think your understanding of it is fine.
The Express can plug into a switch and the switch is plugged into the AE. That is the same as the express being plugged into the AE direct. Switches are transparent devices. (managed switch is slightly different of course).
By the way, something else interesting I have noted: only the 2nd generation AP Express has the DNS problem. The 3rd generation seems to do OK, it will occasionally drop out briefly (no DNS errot) but reestablishes itself before I can do anything about it.
I do not use expresses.. to me they are lightweight AP that just do not not it.. other than the audio out .. they are not useful. A Gen4 or Gen5 AE from ebay is hugely superior router.
However I am happy to work around the issues.. I have certainly had them and repaired them.. dead power supplies are my speciality and Express are expert at dead power supply syndrome.
I am just not sure what you are calling gen1, (The G wireless model?? A108x)
The first N wireless as gen2 (A1264)
The second N wireless as gen3 (A1392)
There is some differences in how people number them.. so it can be better to stick with the actual model numbers.
Apple released an updated A1392 maybe with a different part number..
There is actually a different firmware.. 7.6.5 which is used by this most recent express.. the identical looking earlier one is 7.6.4 firmware and cannot be upgraded. Exactly what Apple have done or the difference I am not sure.. I can check in the xml upgrade file and see.
How do I upgrade an airport express to 7.6.5 firmware?
No it is not in the version file.
Can you please do something for me.. Open your airport utility and go to your latest express and check if it has a Diagnostics and Usage button available.
It may not. My Gen4 TC and Gen5 AE do not.

There is a line at the bottom of configuration.

This tells me the actual ID of the apple router.
119 is Gen5 TC.
See if your latest Express has an ID.