Why was the poet Homer in hell in Dante’s Inferno? Which level of hell is he in? What is his eternal punishment? What was his sin? Why is this surprising?

The first circle of Hell in Dante's Inferno is described in canto 4. It is called Limbo. The people in this circle are not suffering in the manner of other denizens of Hell, because they are not bad people—just people who were not baptized. They are those who were born before the birth of Jesus, or people from non-Christian countries, and thus had no opportunity to be saved. Many of the characters of the Old Testament and classical antiquity inhabit this level, as it contains the souls of all virtuous pagans.
Here, Dante has the opportunity to converse with many ancient writers, such as Homer, Ovid, and Horace, and philosophers, such as Plato, Aristotle, and Seneca. The inhabitants of Limbo have not committed any particular sin to be put in this place. They merely were born in the wrong place and time. They are not actually being punished but, rather, are unable to get into Heaven because they are not saved. Although they are not really happy, they are not being pushed in the manner of the other inhabitants of Hell, as they have done nothing wrong.