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Organic products, like bt or neem oil, will help with these pests.

This article should help: https://www.gardeningknowhow.com/ornamental/flowers/sunflower/growing-sunflowers-in-your-garden.htm

It sounds like they have a fungus. Treat them with a fungicide and that should help.

I am not sure if this is the reason for this is but have you thought of butterflys because a lot of my vegetables are in a similar situation but I have several neighbours who grow plants to encourage butterfly's and when I remove the cover nets they seem to appear but when covered they disappear it may help if you put a fine mesh netting over the plants.

I would try neem oil, which is safe and effective for most insects pests. Most garden centers, including Lowes and Walmart, carry the product. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

There are actually a few pests that like to nibble on sunflowers. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/flowers/sunflower/sunflower-problems.htm

You could try treating the plants with neem oil. This will take care of most insect pests and is a natural fungicide too. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm