A pressure reducer looks slightly like two bells (this is very crude) with the mouths kissing. That is to say, the one is right side up, the other upside down. I don’t see anything like that here. I’m not going to even try to describe a backflow preventer, although maybe I ought to include one in the Lingo section. At least, nothing gets kissed.;) Don’t see that, either.
As to the hot and cold piping, that’s convection. Heat will rise out of the tank until the flex line stops rising and makes a turn, which yours does.
But the main issue here is thermal expansion, which we think is making your T&P valves leak. There is a simple test for that. Get a water pressure gauge, put it on the water heater drain valve, or any hose bibb, and then, making sure nobody accidentally uses hot water, make the tank fire. That might be done by turning the thermostat down for awhile, then back up, or by running hot water until you know it’s firing, then close the tap. Then watch the valve.
Normal pressure is anything below 80 psi. If it spikes much beyond that, then your T&P is doing its job and you should think about an expansion tank.