So turkey eggs require another ingredient to be cooked? That might explain it as I have cooking turned off for all plants so maybe they are just being eaten raw.
Just butting in: eggs are solid food and can be cooked with other eggs. A "stack" of food items, no matter how large, only counts as one ingredient when cooking, so if all you have is a single stack of turkey eggs, you can't cook with that. But if you have, say, a stack of turkey egg [12] and a stack of turkey egg [14], you could cook them into an "easy meal" - turkey egg biscuit [26] would be the result.
Case in fact: "This is a stack of 30 exceptional prepared guineahen egg roast. The ingredients are masterfully minced guineahen egg, exceptionally minced guineahen egg, masterfully minced guineahen egg and exceptionally minced guineahen egg."
As to original post: you should make sure the seeds you have are actually available for planting - if they're kept in a barrel, they'll be unavailable most of the time, greatly hindering your farming - and that your farmers have the necessary time to do that job: if they have all hauling labours activated, they'll often get tied up in endless hauling chains and never plant. Farming may not be glorious, but if you have specialised farmers, you need to
treat them as specialists, planting can't be done as spare-time job besides full-time hauling (i'm emphasising this because it's the error that i'm most frequently committing).
"each farm tile seems to grow one plant at a time" really sounds like there's an organisational problem getting the farmers to farm in the first place, and the most common culprit is Seed Barrel, Destroyer of Fortresses.