Are there other parts of a Lobster that are edible apart from the Tail and Claws?
The only parts that you need to avoid are the intestinal tract - the black line that runs through the tail, and the sac right behind the eyes which includes the brain, stomach, and other organs.

The tomalley is the edible yellow-green pasty substance which serves as the liver and pancreas. However, there are advisories in place by US federal and state agencies advising against eating the tomalley of Atlantic lobsters due to the high concentration of toxins present. I've eaten it before if that matters; it's delicious.

The roe present in female lobsters is also commonly eaten.

Anything else is edible, but not frequently eaten.