First impression and how effective it can be plays an important role in communication.
It's a sentence from a mock exam held in Iran. To me, the sentence is not well written. Here's my revision:
A first impression (or First impressions) and how effective it can be play an important role in communication.
Well, It's a compound (plural) subject, consisting of two distinct things, the impression and how it is received. So the verb should be plural.
One of my colleagues, however, disagrees that a plural "play" is required here. This is because the conjunct is somewhat lopsided. He says the sentence is about an impression and one of its characteristics.
What do you think?