Did Rome intentionally build an empire or was its empire an unintended consequence of its attempts to defend itself?

Answer 1

It was a combination of both.

Expansion - of political and social power, of control over greater areas - is always a predominant thought in the minds of leaders. So conquering the neighbours is a natural progression from this need.

However, when you start fights you make enemies. When you fight these enemies, someone has to win at some point. When you win, you take control of many areas controlled by that enemy. Hence, defending itself lead to gaining more territory from its aggressors.

The final result is that the places under Roman dominance grew until one could not help but consider it an empire, as a collective of areas controlled by one central and dominating group. This collective had grown both on behalf of expansionist and aggressive policies, and as the outcome of defense from outside attackers.