what is "see" in here?

What is the difference between "varies from A to A" and "varies by A"?

When we say something varies from A to A those two things are being compared to each other. So here varies from country to country means we are comparing different countries to each other. However, varies by means we are focusing on the cause of variation and not comparing anything. Ex: Each country varies by population size.

Is "crag" same as "cliff"? It seems like at the beginning of the video, the narrator said "cliff."

Yes, that's correct. They are synonyms for each other, and in fact, a crag is a type of rocky or jagged cliff. The speaker has most likely used "crag" here to diversify his word choice and make the story sound more interesting. Generally, "cliff" is used more commonly. Ex: The group slowly hiked up to the top of the cliff. Ex: There was an eagle's nest on the rocky crag.

What kind of test is "SAT"?

The SAT is a standardized test widely used for university admissions in the United States of America. The SAT is typically taken by high school juniors and seniors and is intended to measure literacy, numeracy and writing skills that are needed for academic success in university.

Would it sound awkward if I say "pleasure" instead of "joy" in this context? If so, what's the main difference between these words?

It might, yeah. Here, "pleasure" would just be a bit too formal. But "pleasure" also has a couple of other meanings, which might make it awkward. "Pleasure" can mean entertaining or to have sexual enjoyment. Whereas "joy" simply expresses the emotion. You could, however, use "happiness" in this context. Ex: Seeing her message was instant joy to me. = Seeing her message was instant happiness to me. Ex: I get a lot of pleasure from watching you suffer. => entertainment

What does “could have + past participle” mean?

"Could have sworn" is used when someone feels sure about something even though it appears not to be true. In this case she was sure where the hive was but it is not there. Ex: I could have sworn I’d paid that bill. Ex: I could have sworn that I left my keys here. We generally use could have + past participle when we want to make a guess about something that happened in the past. This is used when we don't know if what we're saying is true or not true. We're just talking about our opinion of what maybe happened. Ex: A: Why is Kate late? B: She could have forgotten we were meeting today.