How many continents did the Romans conquer?

That's difficult to answer, because back then there weren't countries the way we think of them. Caesar conquered Gaul - basically equivalent to modern France - but Gaul was a region, not a country. They conquered Rumania, but it wasn't a country, either. Egypt was perhaps the closest thing to a country, because it had been its own kingdom or empire for centuries. Of course they took Italy, but that was a collection of little cities and kingdoms. They conquered Spain as a side effect of the war against Carthage, but Spain wasn't just one country, either.

Other conquests covered parts of modern countries, such as in England and Libya.

So it depends on what is meant by the question.