You're sorta kinda in a bit of trouble here. This system is close to being good, but because of a seemingly minor screw-up, you're going to have major problems here. The recirculating pump SHOULD NOT be connected to the drain.
First off, it's quite possible that the segment of pipe between the pump and the "tee" attached to the drain valve is completely or partially clogged with (corrosive) scale/sediment buildup. Judging by the scale buildup on the outside of the pipe just below the tee, it looks like the tee is leaking (why? corrosion?). I can only imagine that the inside is worse. Even the check valve and the ball valve upstream from the pump look like crap. In fact, I'm pretty sure that's calcium on the ground below the check valve (thing between the pump and the drain with a hex bolt -shaped top on it), indicating that it too is already leaking. The check valve almost certainly isn't functioning properly (check valves are intended to only allow water to flow one way,) which is possibly why you are having to constantly readjust the temperature in your shower. The cold water gets injected into the tank at the bottom (via a long "dip tube" that enters at the top and travels down to the bottom.) If this check valve is being held open by sediment, or if it has failed due to corrosion, then cold water could be coming out of the water heater from the drain at the bottom, making your "hot" water turn merely "warm" after about 10-15 gallons of use, which is one possible explanation for your "shower get[ting] colder during use" problem.
My advice would be to get this junk removed ASAP before something bursts and you have a disaster on your hands. Get rid of it completely, or if you want to get it fixed up, get a new pump (Grundfos makes great pumps, but I can't imagine that this pump is usable at this point) and tell the plumber to connect the recirculating pump to the T&P relief valve inlet, which is not currently being used(?), rather than the drain. Doing this would reduce the scale/sediment buildup greatly, which happens mostly near the bottom of the tank. Replace all of the pipe in the vicinity of the pump as well, as it is probably completely scaled up and corroded. Everything else should be ok.
I see a line (the CPVC that goes into the wall) for what I hope to be a T&P valve, but I can't see where the actual T&P valve is. If it's tee'd off of the hot water outlet, then that's fine. I'd hope it's not simply laying on top, not connected to anything, but I don't have enough faith in whoever installed this to take that for granted.
Somewhere at the end of the line there should be a valve that bridges the hot and cold water lines, which is usually under a sink. If that valve fails or is installed backwards then you will get excessive hot water in the cold line.
To test the valve:
- Find the sink with the valve under it.
- Close the cold water valve under the sink.
- Open the cold water faucet.
- Water should SLOWLY come out of the faucet. (If it comes out quickly, you have a bad valve.)
- When the water warms up, the flow should slow down and eventually stop completely. (If it does not stop then you have a bad valve.)
Best Answer
Here's a diagram of a hot water recirculating system
As I understand it, the idea here is that the recirculating system runs hot water around the pipework to keep the temperature hot near the faucets/taps. This allows for instant hot water at faucets/taps far from the water heater.
Even when no taps are running the pump should be actively maintaining the circulation as needed. It needs to do this as any unlagged pipes will cool the water in them if no faucets/taps are drawing hot water.
When the water near the faucets/taps is sufficiently hot, the "Aquastat" will turn the pump off.
Your power feed to the recirculating system should be via a timer, or other device, that lets the pump run whenever the "Aquastat" feels necessary. This should be "on" during any times of the day when you are likely to use the faucets/taps.
Some ideas:
You should be able to test this with a thermometer and a voltmeter if you can locate the "aquastat"