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#2 is factually incorrect.
Any time you add a liquid into the combustion chamber, the act of vaporizing that liquid will reduce the peak temperature of the mixture captured inside the combustion chamber. Due to Boyle's law, this will also reduce the peak pressure, and cause the process of extraction of mechanical energy to become less efficient.
And if you add enough water to the incoming mixture, you'll just quench whatever combustion does occur.
The entire idea behind water injection is to cool the charge mixture enough to prevent detonation and/or preignition. This makes it possible to safely force in more charge mixture than would otherwise be prudent. Yes, it also means that water injection also allows a higher compression of the existing charge mixture than would otherwise be prudent.
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