Learn Russian: Если бы не их профессионализм, мы бы провалили задание. - If it weren't for their professionalism, we would have failed the task.

You are exactly right that negation often triggers the Genitive case. However, the fixed phrase Если бы не (If it weren't for...) is a special exception. It directly takes the Nominative case for the noun or pronoun that follows it. That is why we use the Nominative профессионализм rather than a Genitive form.

Why is the particle бы used twice in this sentence?

The particle бы is used to form the conditional mood. In a full hypothetical situation, you need it in both halves of the sentence: once in the condition clause (Если бы не, meaning 'If it weren't for...') and once in the result clause (мы бы провалили, meaning 'we would have failed').

Why do we use the perfective verb провалили rather than its imperfective counterpart?

The perfective aspect is used because the hypothetical failure is a single, completed event. They are talking about one specific task that would have had a final, unsuccessful result, rather than a repeated or continuous process of failing.

Is there a difference between using задание and задача in this context?