PD, I would like to see if you can take a pic of one of the sick fish so I can get a look at it. Ich is a parasite, It has an appearance of salt being sprinkled on a fish. You mentioned milky slim, To me that puts a red flag up either chemical reaction, or bacterial infection. I think Billy is on a great track of things to be concerned with and easy cheap and pro-active ways to assist your pond. KH seems low to me, Low ph and low KH can mean a unstable environment for the fish. The more stable the environment the less stressed a fish will be and therefore the more chance it has to fight infections on it's own. KH can be raised slowly with oyster shells, but it can be also raised quicker and more precise using regular baking soda. I would recommend adding several table spoons at a time. About a hour after adding check your KH until you reach a reading of between 120-160. at this time you should see the PH become more neutral or slightly alkaline (7.0-8.0) this is a better range for PH, but PH isn't particularly important as long as it's stable. KH is what makes PH more stable.
From what I'm reading I would also be concerned about chemical reaction. Do you know if your water being put in the pond has Chlorine, chloramine, none (Well Water) ettc. and are you treating the water according to your source water. I have seen more than one hobbyist treat their water and use a declorinating product when they actually had chloramine, the chlorine neautralizer didn't bind the left over ammonia and it ends up leaving a fish with a almost burned effect. (White slimy skin coming off)
Now for the Oxygen questions. Under normal circumstances I think you probably have plenty of oxygen in your water, but in times of stress, more oxygen just make it again easier for fish to fight off stress related issues. so adding more surface water movement or adding air stones is simply helping and not hurting anything. Fish lying on the bottom just before dying tells me stress, but if they were needing oxygen they would probably be gulping for air. so for now I don't think lack of oxygen is a primary concern but again, never hurts to add air.
Have you added any salt? many have mixed opinions on using salt, But from experience, when having questionable problems and there is a skin issue, salt can help a fish build slim coating. So adding 1# of salt per 1000 gallons will not hurt anything and may help some. At least might buy some time until we can figure out what exactly is going on. your pond is a very young pond, maybe cycled but not balanced as far as fish load to filtration factor is concerned. That could still take several months to become completely stable. On your size pond I wouldn't have added but about 10-12 fish for the first 2-4 months then only would have added one or two a month until I reached a balance between what appealed to me and what the filtration system could handle. Throw the rule of 1 inch of fish per ten gallons of water rule out the window. I do not agree with this statement at all. It depends on what YOUR filtration can handle not how many inches per gallon. I have seen way to many ponds fail with 10 fish of 10" in 1000 gallons than I can count, WHY, they simply didn't have enough filtration to handle that kind of load. But on the other hand I have seen 4-24" koi live in perfect harmony in a 2000 gallon pond, One that had a way to remove waste, had plenty of oxygen, stable temp, minimal ammonia, nitrite, and nitrate, and the water kept up with.
On your test kits, Strip tests are really not the best choice for a novice, they simply are not that accurate and can give false readings to an inexperienced eye. Liquid drop test kits are far more accurate and far better to learn from. American Pharmaceuticals Inc sells a good master kit that has everything you need in it except for the KH and GH test kits, API also makes them too but they are sold separately. The master kit can be purchased for around $30 the KH kit about $7 GH is about the same but really not needed as much as KH. Learning how to adjust water and why, and also learning what is good water and what is GREAT water is very important to fish keepers, Koi can and are very easy to stress in water that is less than ideal. But Keeping ideal water does not have to be hard, you just have to take the time to learn how to keep water, then fish keeping starts to become easy. LOL
Sorry to hear about your losses, and I hope we can help get you back under control and stop losing fish. But keep in mind, The pond is new, there is/was a pretty good load of fish in the pond during start up. your not the first nor will you be the last to go through what we experienced keepers call new pond syndrome. the most important thing is to keep trying to learn as much as you can and it will get better. BTW, on water tests, I recommend new pond keepers to start testing twice a day, once in the morning once in the evening. this will help find what PH swings your experiencing, then go to once a day, this helps establish what the Ammonia, nitrite and nitrate are doing, then test at least twice a week one your going, this gives you a chance to spot a problem before it becomes a problem to the fish. Also, Keep a journal, That way if there is a problem you can post for others to see and you remove that water quality problem out of the way and can see what's going on for your self, and gives those with more experience a better chance at diagnosing a problem from what else it MAY be?