What are the chief features of Etruscan culture and religion and what light do these features cast on the problem of the Etruscan’s origins?
This is a great question. The biggest problem with studying anything when it comes to the Etruscans is that they lived so long ago. In other words, very little that is Etruscan is left for us to study. Moreover, they were absorbed into Roman society. For this reason, it is very difficult to speak of anything Etruscan. And when we do, it is usually mediated through Roman sources. In light of this, we can say that there is a problem of sources.
Here are some points about Etruscan religion.
First, the Etruscans were polytheists. Moreover, according to Pliny, the Etruscans deified objects, such as lightning.
Second, the Etruscan were known for their divination. They sought the will of the gods through various means, such as examination of lightning. However, the most famous was through the inspection of entrails. A seer, called a haruspex, would look at the entrails of an animal and figure out the will of the gods. The Roman practiced this as well. They called it the Etruscan discipline.
Apart from these points, it is very difficult to say anymore about the Etruscans.