The BBC puts out a podcast called "In Our Time" that features a panel of three historians and a moderator discussing a wide variety of historical topics, from King Tut to WWII. I've used them before as supplemental or extra-credit assignments.

As far as popular histories, I've also used excerpts from Thomas Cahill's books about the ancient Greeks and medieval Europe, as they tend to be written in an engaging style that can get into specific stories. Again, not main content, but a nice bit of "spice."

Yes. In particular, I like using "popular" sources that serve to show things that we can often only narrate indirectly in class. For instance, the documentary Breaking the Maya Code does a better job than I could ever do of explaining the process of decoding and interpreting an ancient language, and what that says about about how the modern understanding of the Maya has evolved; my job there is simply to make explicit concepts like historiography and historical models so that they can see how straightforward jargony abstractions can be.

Unfortunately I have a tough time with podcasts because they're not really something I listen to on a regular basis; the closest thing I've used to that format are excerpts from The Teaching Company/The Great Courses, but I'm not sure what space they inhabit between popular and regular history.

As to your second question, I think of popular history as much like what the mechanics who fix my car do when they give me a general sense of Part X doing Y which leads to Z. They are not actually telling me how things work or how they see my car and its internal process, but rather providing a simplified map or model that makes a glimpse of what's going on accessible to me.

These models/maps are really important, and exciting ones are worth their weight in gold even if they are wrong. I like to use them as the lede for new concepts or blocs of history, and then steadily escalate the level of deconstruction over the course of a semester until it's routine to apply formal historical methodology to them. The idea isn't to debunk or, worse yet, sneer at the "popular" approach, so much as make clear its limitations and provide tools to students so that they can address them. After all, people who reach general audiences probably did something right, and it's incumbent upon academics to use that to their students' advantages.