You only want to work on solving one issue at a time, so for now......power off the AirPort Express and work on getting the AirPort Extreme working correctly.
Users often make the mistake of setting up the AirPort Extreme to "Extend a wireless network" when they connect it to another router using an Ethernet cable connection, so the first thing to would be to check some settings on the AirPort Extreme to make sure that things are set up correctly.
We assume that you have already tested or swapped out the Ethernet cable that connects from one of the LAN <--> Ethernet ports on your modem/router to the WAN "O" port on the AirPort Extreme, correct?
If not, that would be first thing that you would want to do. Temporarily, for this check, connect your Mac to the Ethernet cable from the modem/router and turn off the WiFi on the Mac. Run a few speed checks that way to make sure that the Ethernet cable is delivering the correct speeds from the modem/router.
Next, connect the Ethernet cable to the AirPort Extreme and check some settings on the AirPort using AirPort Utility on your Mac. Open up the utility and click on the picture of the AirPort Extreme, then click Edit in the smaller window that appears.
Click the Wireless tab at the top of the next window and make sure that the setting for Network Mode is set to "Create a wireless network". Unless the AirPort Extreme is at least a room or two away from the modem/router, you should not set up the AirPort Extreme to use the same wireless network name and password as your modem/router.
Next, click the Network tab to make sure that the AirPort Extreme is still set to use "Off (Bridge Mode)" as this setting can easily change without your knowledge when you are making other changes on the AirPort.
Once you have checked the settings on the AirPort Extreme, make sure that the WiFi is turned off on your Mac again and connect the Mac to one of the LAN <--> ports on the AirPort. Run a few speed checks that way.
The reason why we are checking Ethernet speeds first is simple. Unless Ethernet is working correctly, wireless will never work correctly.
If you are now getting good speeds when you check using an Ethernet cable to the AirPort from your Mac, turn the WiFi on your Mac and check that connection with your Mac in close proximity to the AirPort.
Report back on your results.