if you can find some Koi that are not real expensive they eat duckweed, it takes the grass carp a little while to get going , if I remember right you will need 10 to 12 per acre
Grass carp could be an option , also if you fertilize the lake it will cut down on the light penetrating in the water and will kill it. you need a good professional for some solid answers
Iceburg has no value but some of the other ones are really good for you and no you can not grow rice wheat of beans in a small area and get much from it , @kuduman this is some of what I grow
you can grow, water cress. kale , sunflower micro greens , and any of the red or purple lettuce has a lot of nutrients , with a little research and planning its surprising what can be grown in a small space , I been doing it for years, A few guys from here can tell you how much I grow in a...
I had Brussels sprouts ,Broccoli , cauliflower Cabbage ,carrots growing all winter some of the cold weather lettuce , just planted this week about 5000 onions and a couple hundred red cabbage will be planting tomatoes in 2 or 3 weeks, All grown from seeds