Which is a dependent clause?

during intermission, while we were discussing the performance
dodging frantically, a valet ran through the crowd and into the theater
dashing after him, two police officers plowed through the lobby crowd
discussing the commotion, we decided it was more exciting than the play

The correct answer is - During intermission, while we were discussing the performance.

A dependent clause is one that cannot stand on its own - it has to be a part of a larger, independent sentence in order to make sense. Dependent clauses are incomplete, and therefore they need to be extended into a larger sentence. The only dependent clause among those above is sentence 1, whereas the rest are complete and therefore, independent. 

The first clause is a dependent clause. That is because it makes little sense if used on its own, while other clauses can stand on their own and make sense.

Because the vietnam war was fought in an especially brutal and untraditional way

Objective pronoun is the answer.