I have no other applications open while I'm doing the installation.
Yes, you have. As the message from the installer says, you have Couatl.exe still running from the previous FSX sessions, most likely because you launched the installer too quickly after having quit FSX, not allowing enough time for all the executables launched by FSX to quit, close all files and release all locks.
The installer TRIES to quit the program automatically, but it doesn't always succeed, which is why you get the subsequent errors.
Either try again after a Windows restart, or use Task Manager to Terminate the Couatl.exe program before starting the installer.
