Extending wireless network slows both wired and wireless network speeds.... dramatically

So now I'd like to add a third WAP using an Airport Express with a wired connection to the primary Airport Extreme. I assume I should do the same and NOT extend the wireless network?

That is correct. In fact with wired connections you are not limited to using Apple base stations. Any wireless access point can be used. This configuration is known as a "roaming" network.

Should Apple devices on the wireless network automatically switch WAP based on signal strength?

In theory, yes. In practice, not always. iOS devices, in particular, have more "trouble" automatically switching ... but that's by design to help prevent dropped calls when roaming. Sometimes a simple, toggle of Airplane Mode, solves this for those more stubborn cases.

When I have both Airports set to create their own wireless networks, everything works fine.

This is the correct setting. "Extend a wireless network" would be used only if the AirPort was connecting using wireless......but you are using Ethernet.

Another way to say the same thing would be to state that whenever the AirPort has a wired Ethernet connection to the network, you would use the "create a wireless network" setting for that AirPort.

My home network has 3 AirPorts. All of them are connected together using Ethernet, and all of the AirPorts are set to "create a wireless network" that uses the same wireless network name and password.

I have switched back but to each creating their own wireless networks and everything is working fine but I'd like to have one extended network throughout the house.

You will have an extended network if you configure each AirPort to provide a WiFi network that uses the exact same wireless network name and password. When AirPorts are all connected using Ethernet, this type of network is technically called a "roaming network". This is the best performance option in terms of signal strength and speed......much better than a network that uses extenders that connect using only wireless.

Should Apple devices on the wireless network automatically switch WAP based on signal strength?

In theory, yes. In practice, this is not always the case. For example, Macs will usually do a very nice job of automatically switching to pick up the highest quality signal from the closest access point as the Mac moves about the house.

But,.....iPhone and iPads will not normally do this. They might switch from one access point to another.....and they might not. Nature of the beast with iOS devices.

I have a 5th generation Airport Extreme connected to a Comcast cable modem using DHCP and NAT. Connected to that I have a Airport Time Capsule (3rd generation) in bridge mode. When I have both Airports set to create their own wireless networks, everything works fine. However, if I switch the Time Capsule to Extend A Wireless network and select the wireless network from the primary AirPort Extreme, the entire network dramatically slows.

If the connection between the AirPort Extreme and the Time Capsule is a wired one, then you DO NOT want to reconfigure the Time Capsule to "Extend a wireless network." This setting is only when the connection will be wireless.

With both set to "Create a wireless network," and both base stations configured to use the same Network Name, wireless security type, and password, you already have a "single" extended wireless network that will have significantly better overall bandwidth performance over an extended network.