The valve on the side tank is a T&P valve - the fact you can open it is no perfect indication that it's good.
A mixing valve would require both the hot and cold to connect to it (it's called a tempering valve). I'm not sure, but I think it's a pressure relief valve (again, not a PRV). It could be defective, or could be doing its thing...it would normally be set lower than when the T&P opens. If you have an expansion tank, it could be shot. The city could have raised the supply pressure (new pump, or new water tower, for example).