In gernal I don't think any plant does better by cutting off live green material. Most plants that are adapted to winter have ways to pull nutrients out of the green part and store them in bulbs, roots, etc.
People love to give advice. People who have some basis for their advice won't mind explaining what they expect the salt to correct, which means they also can tell you all the details. But in most cases they're going to say "I heard it somewhere" or "it helps them" or other silly things that lets you know they have no idea. If they do have a theory and can explain it then at least you have some basis to make an informed decision.
I hope the people telling you to add salt warned you of the risks, explained the amount to add and for how long. Also hope you have a salt test kit, and have a way to dispose of the salty water safely, and don't have a problem doing the large water changes needed to reduce salt levels when the treatment is over.
There's no huge problem adding salt if done correctly. Fish can normally live thru it.
If you're adding salt only because someone said to, no additional info, you might consider what path that puts you on.
Interestingly the buoyancy issue could go away during the treatment...on it's own. But the salt will get the credit.
Unfortunately buoyancy problems can be many things. Can even be something silly like they ate a piece of styrofoam that was small enough to swallow, but too big to pass. Very unlikely, but just can be lots of things.
The fish doesn't bob to one side or the other? To me, and this is purely opinion not science, a fish with gas in the gut will be on its side sometimes, have trouble keeping upright, because the gut is in their underside. Also, because this has lasted so long I wouldn't be thinking gas, virus, bacteria...doesn't mean it couldn't still be these things...just guessing.
Feeding peas was a good idea. It's safe and can work for some causes. Always worth trying.
Loved that finnipper suggested not using salt and you took that advice. In so many pond forums salt gets thrown at everything.
Sinking vs floating food wouldn't matter. Both foods would be equal. It's the breakdown that causes the gas, if any. Or blockages. However, you could give the fish more vegetation. Only a very small chance it could help, but at the very least the fish would probably enjoy it.
I don't have any cures to suggest. Feeding peas is about all we have short of taking the fish to a Vet for xrays. But even with an autopsy these buoyancy problems often remain a mystery. I've cut open more than a few fish that had problems like these for a long period and always think I'm going to find something obvious but haven't yet. I usually just say "it's genetic" which is my way of giving up and just let the fish live out its life.
The sun burn is the main unfortunate problem at this point. Adding shade is the only help I can suggest for that.
I see where Tyne & Wear is now, I checked climate and if I have it right the avg low is about 0C in the coldest part of the year, with max recorded temps getting almost to -20C? If so I would consider that a mild climate. The record lows would be for very short periods. I wouldn't be too concerned.
It is true that unless the pond is covered by ice there isn't thermal layering. But with ice cover there is, which is why ice forms at the surface. The water below the ice is higher than 0C. Because the ground is warmer 4C water will be found near the bottom of the deepest point.
If you build a shelter over the pond to keep it a little warmer, in your climate, you should be aware of something called ?Aeromonas Alley?. When water temp is between 5.5 and 16.5C the fish's immune system isn't working very well while Aeromonas and Pseudomonas bacteria grow well. So if the fish get an infection for whatever reason it can be deadly. If you can keep water temp above 16.5C that would be great. But if your shelter keeps the fish in the Aeromonas Alley it would be better imo to open the shelter and let the water temp drop to below 5.5C.
60 cm deep ponds with Koi are very common here in the US, even in extremely cold areas, day time highs not getting above 0C for long periods. Deeper is better for lots of reasons, but it is commonly done.
Water Lettuce, Water Hyacinth and Water lilies would not be oxygenators for the pond. When the sun is out they would release O2 into the air. Their roots would consume some O2 in the water (not a lot, not worth being concerned about).
Healthy underwater plants, like algae, do oxygenate the water when the sun is out. But at night they consume O2 and produce CO2. Plus any decaying plant matter would consume O2 and produce CO2 day or night. So even though some plants are called oxygenators they're not really a benefit, O2 wise, since if there was an O2 problem the fish couldn't make it thru a night of really low O2.
I don't know where you live, climate would really affect the best options. So I'll just say some general things.
Yes, 10C (50F) is a good guideline to stop feeding. But it's not digital meaning 9C is certain death and 11C is perfectly fine. It's just a guideline people kind of all said if we have to pick a number, 10C seems reasonable.
As water gets colder the fish's systems slow down and they don't digest food as fast. The thinking is if we feed them a lot of food they could end up with a gut full of food which can cause problems. Just like some people have digestive problems and have to not eat too much, and/or too much of certain foods.
There are easier to digest foods (wheat germ based) that can be fed down to say 4.5C (40F). But most people don't bother, fish are OK without it.
If the water warms up (not the air) the question to ask yourself is what do you think the water temp will be over the next few days (including night lows). If it's spring you might start feeding when the water temp is 5C because you expect water temps to rise. Or you might play it safer and wait.
I don't go too much by water temp. If fish are active, seem to be looking for food, I might give them some, but in winter I won't give a lot. My thinking is there is food in the pond...algae, bugs, so fish do eat. I assume, like us, if they already have food in their gut they wouldn't eat more. Never believed Goldfish eat until they pop. However, I've been around pond fish a long time. I started slow, fed a little, see what happens. Next year a little more. And I do it only because I like too, not because I think the fish need it.
So the standard line, and I think it's reasonable, is to stop feeding at 10C (50F).
Whether to turn the pump off or on is a personal choice that should be influenced by climate.
In really cold climates there isn't a really good choice. The negative is when ice covers a pond gas exchange slows down (basically stops) and O2 drops and harmful gases increase. Fish load and the amount of decay determines the risk. I'd say for most ponds maybe ice covered for more than a month starts to be a concern. But it's not like a day or a week is a problem. Running a pump can keep at lease some hole for gas exchange in the ice unless the air drops too much for too long.
The plus side to ice covered pond is that it can keep fish warmer. Most people know warm water rises, but that's not entirely true. Water at 4C (39F) is most dense and will sink while water 3,2,1C will rise. Without any mixing from wind or pumps the water at the bottom of an ice covered pond can be 4C. Wind and pumps mix the water, allowing it to cool below 4C so fish can be in 0C water (even minus) water for long periods. Goldfish and Koi can survive much longer in 4C than 0C.
So the unfortunate choice is trying to figure out which is the biggest risk. Things to consider...Cold water holds more O2. Cleaning a pond before winter reduces decaying matter which would reduce harmful gases reducing the risk of ice covered for long periods. Fish load must be considered.
My own opinion is if you live in a climate where it is so cold that a pond is ice covered for more than a month a pump really isn't any kind of fix because it probably isn't going to keep a hole in the ice for very long any ways. So you end up with really cold water (although the ground will heat it back up) and poor gas exchange. Covering a pond is really what people in that boat use. Works great as long as it's not a floating type cover. You want air space between water and cover.
In moderate climates I don't think there's any great danger from leaving the pump on or off. Iced over pond for a few days, a week or two, is no big deal except for the very few people who have really big fish loads. In those climates even with the pump on water probably won't go below 4C (39F) anyways, and even if it does for a night or two the fish can normally handle that unless they're already in bad shape.
Re: Fish problems, need help for inexperienced keeper!!
violet reminded me of something...one of the reasons I came to this forum.
I'm a pond dude for many years, never had an aquarium. I'd bet 75% of the good info I've learn over the years has been from reading aquarium forums and sites. Water Garden keepers aren't too much into testing, data, so myths pretty much rule. Koi keepers are a lot more serious, but I've never found any info that's as good as from aquarists, by far. And it's almost all relatable back to ponds.
For treating pond fish we transfer sick fish to a hospital tank, which is nothing more than an aquarium. From there treatment is exactly the same as how an aquarist would treat the same fish.
The only reason I didn't suggest transferring to a hospital tank is you probably don't have one and a 200 gal pond is about the size of a Koi hospital tank so I wouldn't see a reason for a separate tank. Just look at your pond as an aquarium.
If you search aquarium sites and focus on Goldfish (maybe any cold water fish?), and any help violet and others here can provide, you could do no better imo.