How do I know that what I'm writing about in the first parts of the HAT test is relevant?

In short, there's no way it wouldn't be. The only way to go wrong for sure when taking HAT is to not write down something because you think it's not relevant enough. Although history in high school (for both A-levels and IB) is centred around grand events and the 'wrong' or 'right' answers, history on university level is often conducted by in-depth analysis of the most minuscule details. I once got into a two-hour argument with my tutor about whether or not certain cow-bones found in Ipswich, dating from 6th century Britain, were the result of animal-husbandry or herd-raiding. The conclusion of such an argument could have massive implications on the survival of government in post-roman Britain. Thus, when analysing articles in the first part of the HAT test, it is true that you don't need knowledge of the time periods they originate from- mine were from 16th century Germany and 10th century Damascus, respectively. But what is important is that you force your imagination to fly- every word, every sentence and description, has to be analysed and extrapolated on to the fullest. Even if your examiner does not agree with you, he or she is much more likely to see potential in your analytic abilities, and in the end, it is potential that they are looking for.