1. Unless a larger context disproves it, which I do not think would be the case, it is talking about two pairs of items that one should link together respectively when reading. So, it is not telling the students to relate (1) to (2).
関連づけて読む is not an imperative as far as the form but it certanly functions as one. This form is often used in memo writing and listing.
2. It is the suffix きって that is sometimes written as 切って. It means "the best/most (within the preceding word)", and it has nothing to do with cutting.
3. You are not reading this sentence correctly. In most cases, you WILL have to pay the full amount on your first visit if you do not produce your insuarance card, which is why it says the amount will surprise you. If you bring your card the next time you go, however, they will refund the difference. その日 refers to what you said.
4. It is なれない, not 慣れない. 「 うっかり病気にもなれない。」 means "You can't even get sick inadvertently.", which may sound strange if directly translated. It is saying that it is better if you just do not get sick too often.