Carp vs. Flora

Question
My 1000 gallon pond is about 21 years old. The three large Ghost carb which command the depths are around 24 years old. I had to build a bigger pond to accommodate them! For many years, I struggled to control the plant growth in this pond. Other fish arrived and bred, notably a community of Rudd which once numbered around 25, as well as various other species. Frogs used to be present in abundance-the chorus at mating time could be heard for miles.
Three years ago, I gave up trying to control the cabumba and stuff. I used to haul about 5kg out of the pond each week, just to give the fish some space. I also had to clean the pump and filter about twice each week during the summer. So that we could go on holiday etc, I bought a new pump and an external filter which can handle more water. Although the fish population had already begun to decrease, I have found that the oxygenators have virtually ceased to exist. Lilies grow in the "top" (settlement) pond, but only marginals and reeds survive in the fish-populated area, although even the water hawthorn and marsh marigold are looking a bit sick this year. All of the frogs have gone. I now have only the "Three Musketeers", three mature rudd and "Tinker", a Golden Tench. These seven fish have spent the winter virtually exposed, there being no plant cover (I put a net over the pond in winter to protect from raiding herons). The water is crystal clear for the moment, but I detect eary signs of the blanket weed which has become a problem lately. I run the pump all year round, which has kept the water ice-free for all but a couple of days. I also run a fountain during the summer when oxygen might be a problem. I feed with sticks every day during the season, when the water temperature is above about 10c. The fish all seem to be in good condition-somnolent but mobile, fins erect, no gasping. There is very occasional "dashing", probably due to a minor skin parasite, but this is infrequent. The carp are around 22" long.
I'm at a loss to know how to fix this pond. It looks like a dead zone!

Answer
I'll be able to answer this best in a list of advice.

-Some of these plants may not stay healthy over winter.  Whether they do or not depents on a variety of factors.  Some include how cold/windy it is, how many frosts/snows occur, how trimmed the plants are, and what species, of course.  I would typically buy new floaters and anacharis each season.

-Many plants do get very unruly.  The best thing I have found is to plant most of the plants around the perimeter and stick with floating plants and lilies for the center of the water.  If the taller plants get a good root system going, you can keep their footprint small but still have them grow tall.

-Iused to care for a 2,700 gallon pond stocked with ten 10-15" koi.  I would typically rinse the filter 4 times per week.  If a plant's substrate was disturbed, it would clog the filters within a day and I had to rinse them twice a day.

-If you are seeing unexpected algae growth, it is usually one of two things;
 a)  If you don't perform partial water changes often, it could be a build up of dissolved organic material.  Do a few partial water changes.
 b)  If you DO perform partial water changes, it could actually be your water source that is to blame.  Sometimes, localities' water treatment processes will change, leaving the water slightly different than before.  This doesn't usually affect showering, washing dishes, drinking, etc. but it can drastically change your pond or aquarium.

-Regarding the winter time...The net is a good idea.  You can allow the pond to freeze over as long as you break a hole through a part of the ice for gas exhange to occur.  It is best to run the pump year round.

-If you don't already, checking the pH ammonia, and nitrate levels is a good use of time.

-The dashing is a good thing, as it lets you know the fish are healthy and there is enough oxygen for them to be active.  If they were doing this but grinding their sides against rocks and liner, that would mean potential parasites.

-What you have is plently for a 1,000 gallon pond.  It just sounds like it needs a minor overhaul this spring.  The "by the book" recommendation is 1 full grown fish per 1,000 gallons.  This is very conservative scale and we can do things to allow for overstocking, such as keeping plants, performing water changes, providing shade, cleaning filters often, avoiding overfeeding, and the most important of all...have a large biological filter section that has plenty of high-oxygen water passing through it at all times.