The Holy Roman Empire existed for close to a thousand years, and it changed a lot over time. If you have a specific time in mind, it might help to mention it.

Was it a single country or a coalition of independent realms?

At the beginning (High Middle Ages) it was definitely a country. At the end (18th/19th century) it was in some ways more like a coalition of countries. Officially it was still a single country, but the Empire had very little or no actual power over some of the states.

Were these realms considered kingdoms, duchies, states?

The later Empire consisted out of a number of states - around 300 in the 18th century. These states had different ranks, they could be duchies, counties, bishoprics, free cities, and more. There was even one kingdom - Bohemia.

Who was in charge of them?

Most of them were ruled by hereditary princes (prince is a general term for dukes, counts, and so on). The church states (bishoprics and such) had rulers who were elected or appointed. The free cities were republics controlled by an elite of citizens.

Did the Holy Roman Empire act as a single entity?

Sometimes. The last time it acted as a single entity in a war was the war against the Ottoman Turks in the 1730s. But there had been nasty wars inside the Empire as well, most importantly the Thirty Years war, in which one half of the Empire bitterly fought against the other half.

How powerful was the HRE compared to other European powers?

Depends on the time. Between the 10th and 13th centuries, it was a major power. Later, not. By the late 18th century it was pretty much a joke with respect to power politics, and Napoleon finally conquered it and dissolved it.