Beautiful house / land / pond / dog / deer/ fish ... well, everything! PS, I have black walnuts too... they are hard to landscape around!)
Your fish are common goldfish (the shubunkin goldfish are calico and yours's only red or red/white)
I have a feeling that with the amount of fish (and how big they are), they are too many for your pond. that's why you got lots of muck. But seeme like your biofilteration are doing fine with your fish load so I'd leave that be if you are fine with cleaning the pads out like you are doing. If not, reduce the fish.
The good bacteria that help you convert all the waste fish/environment created lives everywhere under the water (pond liner, rocks, plants, etc, so cleaning the pads out wont hurt them much.
Reduce your feeding or stop the feeding all together and the fish will eats the algae on the side of the pond. No need to get rid of them since they are also help with taking nutrient from the water making water safe for fish. Unless you think it's unsightly you can leave the algae alone. But if you want to remove them, you can use toilet brush to scrape them off. But the algae in my pond comes and goes... I just leave them be.
You can also plants some more plants around the edge (flag irises come to mind) to help take the nutrient from the water, that will help compete the nutrient with algae and help you reduce some.
The amount of fish and the amount of feeding are the reason for your algae growth
You can do water change once in a while to reduce the nutrient in the water. If you do a water change, test the pH of the water first to make sure it's match or similar to your pond. If you use city water, make sure to de-chlorine it too.
make sure not to spray anything that can be toxic to fish up hill so when the rain comes, the run off wont kill the fish. If you put fertilizer for the grass, make sure it's not toxic. If it gets in the water, it can create algae bloom though.
cant help with the filter/pump
sorry.