This is nothing to worry about, the cotyledons, or seed leaves as they are sometimes called, is fueled by nutrients stored within it. As the plant grows and develops true leaves and a root system the cotyledon naturally senesces and falls away as the plant begins to produce its own nutrients.
With regards the weed plant, I'm not 100% sure why it is dying. Probably because the sunflowers are competing with it for water and nutrients. They may also be shading it and starving it of light. Don't worry, it's best not to have any weeds competing with your plants!