how to create AppleScript app to run a set of terminal commands

You don't actually need to use AppleScript for this - just put all the shell commands in a text file and give it a .command suffix and make sure it's executable (e.g. chmod +x my_script.command) - this will make it double-clickable in the Finder.

Yes, you would use do shell script.

However, for the commands where you execute as super user (sudo) you would instead use with administrator privileges. So, for sudo rm /usr/local/mysql you'd do:

do shell script "rm /usr/local/mysql" with administrator privileges

If your list of commands is long, then it might just be easier to put all your commands into a single shell script file, and then execute that shell script using do shell script:

do shell script "/path/to/shell/script" with administrator privileges

I find that .scpt files work best but this is just a preference thing.

Open "Script Editor" and add the following command:

sudo rm -rf /usr/local/mysql; sudo rm -rf /usr/local/mysql*; sudo rm -rf /Library/StartupItems/MySQLCOM; sudo rm -rf /Library/PreferencePanes/My*; sudo rm -rf /Library/Receipts/mysql*; sudo rm -rf /Library/Receipts/MySQL*; sudo rm /etc/my.cnf; say job completed successfully" with administrator privileges