Yes if a trait is incomplete dominance it will be both dominant and recessive :)
An invasive species will often become dominant in which case the diversity index would decrease. This happens when the invasive species pushes out other species as it takes over the area. If the invasive species is unable to adapt, the diversity index would likely not change.
Studying fossils allowed researchers to learn about organisms that lived long ago. The fossils provide as evolutionary evidence that shows how organisms in our present time have evolved over time and which common ancestors they are tied to. Fossils also provide information about climate change depending on the region and location they are found in. Fossils also date back to millenias ago, so fossils dated very far back in the past can help researchers infer that life had existed even farther than what they might have discovered. And finally, by studying fossils, you can determine how the organism may have died.