Hi Joey, good question and this is exactly the right way to ask it.
I agree with you that this one is a bit confusing.
So you are right that they could conceive of the sun of the star, but it would not be correct to say that they fully grasped that it is a star. I think this is reasonably clear from the lecture and just requires you to distinguish between 'conceive' and 'fully grasp'.
However, while they had not fully grasped the magnitude of the universe, they had definitely come to realize that the universe extended well beyond what anyone could observe, so they knew the could not be describing the entire universe. I think this particular answer is confusing, though, so I have changed it in the the quiz and the test to something that is more obviously false according to lecture, viz., "the solar system is not the entire universe, but just a small part of it." (I mean here that it is false that they did not grasp this.)
3 and 4 are not really implications of 2, though 2 permits these possibilities where previously they were perhaps not imaginable.
Of course they had always known that there are many stars in the universe, so this would imply that there are other stars in the universe, but this answer is also confusing because "other" tends to suggest that they grasped that our sun is a star, which they did not. So I have changed this quiz question by substituting "many" for "other". It now reads: "there are many stars in our universe". It is false that they failed to grasp that, and of course false that the ancients failed to grasp that.
Very, very few people imagined that there could be other solar systems. And you're right, this would tend to require realizing that the sun is a star. So since they did not fully grasp that, they did not even come close to grasping this.
Since this is a long answer to your question and the question itself is not well written, I'll simplify for others by saying that the answer as it is written above is: 1 and 3. This is preserved in the slight rewordings of the question as well..