Sorry for not responding earlier. The Fios was cut in my neighborhood and I had no internet, phone or TV all day yesterday. Looking at the gills is of no value at this late stage. The blood leaves them bleached out and not showing much. I don't see any indications of the cause of death in the pictures. Sometimes they just have a heart attack or other cause of death. Stress from pH swings could be a contributing factor.
I would highly recommend you get the KH test kit. A KH value of between 100 and 300 is needed to maintain the pH which will help with the health of the bio bacteria in the filters, which will result in ammonia and nitrite staying at zero, and remove the stress of a pH crash on the fish and bacteria. This level of KH will most likely result in a pH of near 8.3 which is great for the fish and bacteria, but may affect the growth of some plants.
As for the size of the pond, your guess is probably better using the bucket test than the installer. They tend to exaggerate size. Short of using a meter during a full pond refill, the best method of determining volume is the salt test. You can use a salt meter (TDS meter) and measure the salinity of the pond before adding any salt, then using solar crystal salt for water softeners or Kosher Salt, measure the salinity after adding a known amount of salt. There is a calculator at the top of the page to calculate the volume. For your pond, I would start with 3 pounds and if the volume is 300 gallons, the salinity will increase by 0.12%. If it is 600 gallons, then the salinity increase would be 0.06%. Plants really don't like salinity above about 0.1%, but can stand it for short periods, so if the salinity goes higher, be prepared to do an appropriate water change.
Regardless of which size the pond is, it would be too small for more than one or two koi. A general rule of thumb is that a single koi needs about 250 gallons to grow to maturity. They produce a large amount of waste and the solution to the pollution is dilution. Some are successful in keeping more fish but they are fanatics about maintenance of water quality.
Zone 7 A/B
Keep your words sweet. You never know when you may have to eat them.
Richard