Learn Russian: Он говорил тихо, при этом все слушали. - He spoke quietly, and yet everyone listened.

При этом literally translates to "at this," but it is used to mean "at the same time," "moreover," or "and yet." While но creates a direct contradiction, при этом adds an accompanying detail that is slightly surprising or contrasts with the first clause. It sets a simultaneous scene: "He was speaking quietly, and while that was happening, everyone was listening."

Can I use помимо этого here instead, since we are learning about addition?

It wouldn't sound right here. Помимо plus the Genitive case (like помимо этого) means "besides this" or "in addition to this," which you use to add new, parallel information (like adding items to a list). In this sentence, the second part is an unexpected simultaneous condition of the first part. For this "accompanying contrast," при этом is the natural choice.

Why are both verbs (говорил and слушали) in the imperfective aspect?

Because the sentence describes two simultaneous, ongoing processes. He was in the process of speaking (говорил), and during that exact same time, the audience was in the continuous state of listening (слушали). Neither action is presented as a single, completed event.

As a quick refresher, how do I avoid confusing все with "everything" here?