Did you enable DHCP Server on the LAN interface? (See Services -> DHCP Server)
Nope, I don't think I have. Is that the cause of all my problems?
It will be a factor. You said @ryanswj:
I can see the Wireless AP that was created, but no IP addresses were assigned to clients.
If you don't have an active DHCP server then clients won't be assigned an IP address.
Furthermore, why does the WebUI stop responding?
Presumably because you have switched interfaces or reassigned LAN subnet IP address.
If I was trying to make your configuration work I would first make ae0 (wired interface) the LAN and ath0 (wireless) the WAN. Then through the web GUI I would enter wireless configuration details and verify a wireless client could associate (using a static IP address on the client). Then I would choose assign interfaces and swap LAN and WAN (LAN as ath0, WAN as ae0) and reboot through the console.
Wireless configuration can some times be challenge due to signal quality issues and (if your typing is as bad as mine) the challenge of correctly entering the encryption key. I have also found some encryption options don't work well with some clients so its best to sort that out BEFORE making the pfSense LAN interface a wireless interface. It has been my experience that a reboot has sometimes seemed to be necessary to persuade pfSense to correctly behave after major interface related changes such as swapping interface roles.
You didn't explain why you might want to bridge WAN and LAN interfaces. I would be inclined to get it working as a router first. (I have a wired LAN and a wireless LAN bridged together on my pfSense and I need to NAT my internet access so its not appropriate for me to bridge WAN and LAN.)
Is my configuration correct (LAN and WAN)?
I don't have enough information about your configuration to say.