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The result of mixing equal MASSES of water at different temperatures will be the mean of the two temperatures. Unless you are being very sophisticated and are taking the thermal expansion into account, the same will apply to volumes.
No.
Co can mean joint, together or the similar; however it doesn't always mean equal. For example: co-owners in a business are both owners. However, they do not necessarily have to have equal ownership.
If you mean in Excel, yes: you must always start a formula with an equal sign.
The geometric mean, if it exists, is always less than or equal to the arithmetic mean. The two are equal only if all the numbers are the same.