Is sunflower a herb

The suffix -ivore means eater. While herbi- means herbs or plants. -Omni means all. A herbivore eats only plants and an omnivore eats anything. Humans are omnivores since we can and do eating anything. Plants like sunflowers don't eat anything. They make their own food using sunlight.
You really should learn the meaning of Words like these since you come across them over and over again. They actually tell you what they mean.