bash: brew: command not found
Restarting the terminal should have solved the problem since you didn't append what you have typed to a bash start-up file.

Also, even if what you have typed was directed to a bash start-up file it wouldn't affect where bash would find brew since you're prepending to the original path and not overwriting it.

Your problem lays in something else you've done that has changed the settings for your path in a bash start-up file or have deleted/altered the location of the executable.

Why aren't you able to install MySQL? What errors do you get? What form of package are you installing? Is it from the MySQL official site?

Recommended installation of brew makes it reside in /usr/local/bin/. Do you have that in your echo $PATH output? Also, normal brew installation is a simple command that doesn't need brew to start with. So do you mean you get -bash: brew: command not found after attempting the installation of brew?