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I am not 100% certain what you mean by "at operating system level'
It uses a operating system copy module (eg copy, xcopy in Windows).
For a database this may be unreliable because databases are implemented as sets of files that may be in multiple folders or even drives, and that implementation changes from database version to version.
The most reliable way to copy the databases from a MySQL installation is with the MySQL utility mysqldump. It exports databases in SQL scrpts, which you then run on the server where you want the copy to go.
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I couldn't find a my.cnf file on the drive
I'd look again. If none's found, look for inno*.*---that will tell you where the InnoDB files are.
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Therefore, the Church doesn't have any more confidence in any "local IT person with such knowledge" because it is hard to find an honest person who isn't looking for a license to print money.
Non sequitur, indeed idiotic.
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there isn't too much I can't understand about computer programs such as MySQL or operating systems such as Linux if I can find the right person who can give easy to follow instructions.
?! If such jobs could be done with foolproof instruction lists, there'd be no need for DBAs.
Good luck.