Yes, the water comes from your house through that float and valve into the canister. Then from that canister into your pool. But don't worry, your house water is not nasty like that, there's just algae growing in that canister, not in your house water. Once you get the canister clean and give it just a little attention, it should stay clean.
There's no pressure on that return from the pool return to the canister. You could probably plug it good enough by stuffing a rag in it.
Once it is clean, unplug the fitting and turn the water back on. You can then go over to the canister and should be able to make the water start/stop by raising/lowering the white plastic float manually to see if the water starts and stops OK. When you lower the float, water should flow, when you raise the float back to normal pool level it should stop. If it starts and stops normally then you can adjust it if need by by bending that little brass rod/arm a little.
Remember that if your pool is even 1/2" low, it will take a long time for that little water valve to fill your big pool. It only takes a minute to fill a 1.4 gallon toilet tank. You have a 13000 gallon pool.
Hope this clears things up a bit...
Jim