First, yes, you can eat sunflower seeds.
You can also eat the young seedlings, basically the sunflower sprouts
You can eat sunflower leaves if you remove the center rib.
You can eat the young sunflower stalks (in sunflowers where the flower head moves to follow the sun) like you would eat celery.
You can eat the flower petals - they have a really unique flavor. They have the faintest flavor of sunflower seeds, like you got just a hint of sunflower oil or something, but the after-taste is bitter. I had one without noticing the bitter, but just a couple more and it was really noticeable, so just a few petals for color or as a bitter element in a salad is likely all you'll want.
And lastly, you can eat the flower BUDS - "Pick the flowers when they are in the bud stage. The buds taste similar to artichokes. Pull off the bitter green around the bottom of the bud. You may steam sunflower buds or boil them in water for a few moments and serve with butter."
It's a great plant to grow with so many options for what you can eat off of it!