Without wishing to repeat a lot of the advice that has been given, I thought I'd flex my fish muscles for the first time in a year, so...
Unless someone has been overfeeding your fish in your absence it'll be hard to find a culprit.
My first culprit would be the acidity of the water. A pH of 5.5 is too low for most common coldwater carp species. A pH of 7.0 to 8.5 would suit them best, although they can tolerate temporary deviations.
Luckily, if you can say that, ammonia (NH3) becomes far less toxic in acidic conditions as it gains an extra hydrogen ion, becomes ammonium (NH4), and that is insoluble in water, therefore less likely to be a problem.
Unfortunately, raising the ph of the water can free up the bonded ammonia and cause very quick and effective poisoning, especially with a reading of 8 on the test.
What caused the ph crash? It could have been a lot of things. Check your carbonate hardness of both your pond and tap water. KH has a direct influence on pH. If it's low add some crushed cockle shell to the filter system. Dolomite chips or crushed coral (not coral sand as it will cake) can also be used. If your tap water has a high enough KH and pH, start doing small daily water changes to dilute the ammonia whilst bring the pH back into line.
The filter might need a service. Filters can pump out a lot of acid during the nitrification process. Ammonia, as it is broken down (nitrogen/hydrogen) can produce nitric acid and hydrochloric acid, nitrite can produce nitric acid, and if you had a means of breaking down nitrate, that would also produce nitric acid. A breakdown in filteration may have occurred, maybe a power cut whilst you've been gone.
Also, the bacteria that break down waste do not like acidic conditions. They may have slowed and given rise to poisons that have not been broken down fast enough.
All the decaying organic matter in the pond, in the filter will also produce acid as it breaks down. Any plants in the pond (unlikely with carp) will produce carbon dioxide at night, and take up oxygen. CO2 mixed with water produces carbonic acid. Even the fish will produce acids through excretion and respiration. It's unavoidable.
The recent hot weather would have warmed up the pond and lowered the oxygen content. The fish with the greatest demand for O2 would have perished first, starting off a chain reaction - decaying meat, acidosis, poisoning of environment. The more decaying matter there is, the less oxygen available. Breakdown occurs through the action of bacteria that require large volumes of oxygen. The more there is to break down and feed the bacteria, the more the bacteria breed and consume O2, directly competing with the fish. It is a constant battle for survival.
I'm not saying this did happen, I'm just throwing out theories as to why it could happen.
I would also check the fish for signs of disease. Warm weather and weakened animals is a breeding ground for dormant pathogens. Parasites are the first things to strike, normally. White Spot (easy to see- looks like salt or sugar) and Chilodonella and Costia - harder to see, both produce sliminess of the skin which causes the fish to rub and scratch. Death will occur as the parasites spread to the gills and suffocate the fish. Being a water parasite, they can swim from host to host. Quite deadly in warm weather.
Certainly perform water changes - small and regular (daily 10-15% if your tap water is of a decent hardness and pH), using a good dechlorinator/anti ammonia/chlorine/chloromine product, add a water hardening agent to the filter (dolomite, crushed coral, etc) give the filter a bit of a clean - remember to clean biological media in pond water only to preserve the good bacteria, not under the tap - CHLORINE KILLS!
Adding pure salt can help - slowly reaching a specific gravity of 1.010 (brackish) can help against nitrite poisoning and kill freshwater parasites.
These are all remedies that will work but will take a little time. Abrupt changes can be harmful, especially to a fish in an already weak condition.
Keep feeding to a minimum. Use a wheat germ diet to go easy on digestion and to produce less toxic waste product. (in theory) Also it's coming up for winter - wheatgerm is to be fed anyway during cold weather for the reasons above.
As for other things you have said - all fish are ammonia factories. The biggest fish with the biggest appetites produce the most. Goldfish, carp, minnows, all pollute their environment with waste. The environment needs to cope with that waste or it will collapse, kill the most polluting, until balance is restored and life can continue.
50gallons isn't a lot of water for carp or goldies, to be honest. Carp can grow to 24-36", common goldies can grow up to 12" - and they can live for years (oldest goldfish on record was 42 when it died) provided their environment allows them to do so. At fifty gallons, I would recommend a stocking level of four fully grown goldies - that's approx one inch per gallon, to be on the safe side.
Also, incase of a harsh winter, a minimum pond depth of 24" is recommended. Fish will often retreat to deeper, warmer water when it gets too cold. The deeper the better.
As someone mentioned, too much mixing of the waters through movement may be harmful, so turning off filters might be required. Just keep an eye on those water parameters, especially when the warmer weather returns in spring. Having the filter run independently from the pond, and feeding it with an ammonia source during the winter will allow you to keep it alive and hook up to the pond when the weather improves.
Although, in a pond as shallow as yours, the temperature at various depths will be fairly consistent all through. The wind alone will take care of that.
Good luck. I hope you sort out your problem and manage to save the remaining fish.