Most people are going to freak at the ammonia level. That level in most ponds would kill all fish in a very short time. Lots of people are going to tell you do to a complete water change because of the ammonia number. But ammonia is a little more complex than that.
Here comes a lot of info...welcome to the world of having a high fish load. To do it successively does take some effort in learning, testing and treating. Most people in your situation just let the fish keep dying until they have a fish load that can survive the conditions. They love their pets...but not that much.
Safe vs toxic ammonia...
Your ammonia test tested for NH3/NH4 (thanks for that info) which is total ammonia and is more properly called Total Ammonia. NH3 is unionized ammonia and is toxic to fish. NH4+ is ammonium ion and is safe. So the the question is, do you have 4.0 ppm NH3 or 4.0 ppm NH4+? Well we know it isn't all toxic because at 4.0ppm your fish would currently be dead.
There are test kits which tell the difference, Seachem has a couple.
But there is another way. NH3 and NH4+ convert back and forth depending on temp and pH. Lower temp and lower pH drives NH3 toward becoming NH4+. Tables are used. I don't know your water temp...but using
this page and going down to the 4ppm chart, given your 7.0 pH number and a water temp of say 70F, your pond would have 0.017ppm toxic NH3 and 3.983ppm safe NH4+. That's better. But, you''l also notice even that small amount of NH3 is not good. As water temp increases so does the problem.
Ammonia binders...
You've been doing water changes and treating water. Part of those treatments I would assume contained ammonia binders which convert toxic NH3 into safe nontoxic cyclic amine which most kits read as part of total ammonia. So even if the chart says you have NH3 we still don't know if it's toxic. There are kits, like Seachem, which can tell the difference at least for some binders.
You're standing in a tub of gasoline and someone is going to offer you a match...
Without better tests I can't tell if the NH3 present is bound and safe or not. So I'd assume it's unsafe.
Many products are going to increase pH. In many cases this is a good thing as the products buffer the pH to keep it from swinging up and down which is a fish killer. Unfortunately many products won't even say they increase pH or the info is buried. They have to dumb things down in order to sell into the mass market where a cartoon picture of blue pond is as much info as most people want.
In your case increasing pH is the match that will kill your fish. Looking at the chart...if your pH increased even by 0.5 you'd be in a range where you'd expect all the fish to die within a day or two. Even if you have ammonia binder currently in the pond there probably isn't enough to handle that level of ammonia. Be very sure of what you add.
To do list...
1. Buy and add ammonia binder per the directions. Something like AmGuard which is just an ammonia binder. Most products, like what you've probably already used, are primarily used to remove chlorine and chloramine, but have some ammonia binder. The pure ammonia binder can be a cheaper treatment and give clearer directions. But go with what you can get.
2. Don't let a store employee sell you some other "great" product. Not today. At least not unless you quiz them and know their level of understanding at least the basics. You have to know the answers ahead of time, not that the answers sound good.
3. Have a glass of wine.
4. Think about longer term management.
4a. You could add an air pump if you wanted. Making sure O2 is max can keep the fish alive as the damage caused by ammonia can reduce their ability to take up O2. This is more to do with damage already done. In a pond with $$$ fish an air pump is a no-brainer. Feeder fish may be another matter. It's a harsh world. Also there can be a down side. The extra water movement can also drive off CO2 and that could increase pH. I'd probably skip the air pump. Keep things simple. If you saw fish gulping air I'd add the pump and risk the pH change.
Many people suggest water changes to reduce ammonia. Kind of small fix. A 25% is only going to reduce ammonia by less than 25% (new water adds ammonia).
Even more people will suggest to stop feeding. Not bad advice and I would take it. But it's also like suggesting a Band–Aid when you've cut your jugular. Better than nothing, but you still should probably see a doctor. Stop feeding doesn't fix anything today. It does reduce future ammonia, but only reduces the amount, fish still produce ammonia.
So I think binding the ammonia is the best option.
Things may not be that bad, they might be worst...
Your pH is 7.0...how sure are you? Sure it couldn't be 7.3? Test kits are only ballpark. The level of pH also changes throughout the day. That 7.0 if taken in the morning could be 8.5 in late afternoon.
It's strange to measure 0 nitrite with such high total ammonia. It would make me want to double check the tests.
Down the road, after you have control of ammonia, you can research pH buffering.
Longer term...
Once you're confident ammonia is bound there's more to do.
1. Measure KH, GH, and temp. Without that you don't know if you're having pH swings which is almost as bad as ammonia. Given your pH I'd guess KH is very low. Raising KH today will raise pH and maybe kill your fish. But you need to know water quality.
2. Test pH in am and pm. When reporting numbers say the time of day.
3. Add a bio filter...not a toy bio filter, a real grown-up bio filter. You have a small pond but you have the exact same issue the highest end Koi pond keepers have, high fish load. Once the ammonia is bound you have time to research and figure out which would work for you.
Stay away from the crappy worthless combo filters you see everywhere. Let's just make it easy and say all bio filters are worthless, certainly true in your case. The DIY Skippy filters are close to worthless. You need proven, works 24/7, bio filters. These include "Trickle Tower", "Shower Filter", and "Fluidized or Moving Bed Filter". State of the art, butt easy DIY and self cleaning. As in never have to be cleaned. Some people do replace the media in some of these every few years. These can also be placed in very attractive landscape structures like pottery, or built to look like water features.
In your case, because of the water quality, it may take a while to get a bio filter working well. But once you see ammonia drop to zero you will know you have a large enough, and functioning, bio filter.
What's killing the fish...
It's a good bet to say ammonia has probably been killing the fish. There is a time element. The longer fish are exposed the lower the ammonia level is needed to kill fish. Gulping air would have only been an indicator.
However, I wouldn't rule out pH swings yet either. KH will tell that story.