I recall one of my professors mentioning that the people of Mesopotamia drank beer because fermentation sterilizes water. At the time, I remember thinking that beer/alcohol causes dehydration, to which my professor replied that it was likely of low alcohol content. Is any of this true? Did early civilizations use fermentation as a means of disinfecting drinking water?
Secondary question that doesn’t warrant a full post: What was the name of the civilization on an island in the Mediterranean (modern day Greece?) that discovered how to make the color purple and were also very wealthy as a whole?
Is any of this true?
Some of it is. Low-alcohol beer was a common fixture in many cultures, especially since it's a good source of calories - important when you're an agricultural worker putting in a backbreaking amount of work in the day. However, the rest of it is a pop cultural myth which it is my life's work to kill. I'm not casting stones at your professor, even though they should know better; it's a severely common myth. To that end, I commend to your attention my main post on the matter. While it is focused on the Middle Ages, not in Mesopotamia, hydrology is hydrology no matter where.
But the main reason people drink booze over water is because water is boring and booze is fun.
As a bonus, while it isn't quite Mesopotamia, it's close enough in both time and distance, so here's u/Osarnachthis expounding on Ancient Egyptian hydration.
On your second question, I expect that's Tyre, whence derives Tyrian purple. u/XenophonTheAthenian goes more into Tyrian purple here.