It's a really good question. I've never even actively thought about it, but there's definitely a difference in meaning between 'die' en 'dat' in this context and it doesn't really have anything to do with gender of the thing referred to. 'Die' is used for a specific thing and 'dat' is used for a 'general' group/kind of things. In this context 'die' fits probably best. 'Die heeft ze nog niet.'='She doesn't have that one yet.' (she doesn't own the specific title so you can still use it as a gift). 'Dat' can also be used though in a slightly different context: 'Dat heeft ze nog niet.'='She doesn't have such a thing yet.' (it is a book about a certain subject, say fishing, and she doesn't have any books about fishing yet).

Hi I wanted to add that when the word reflects directly on the noun, the rules are pretty strict. So: het boek dat.... de boeken die... You cannot use them interchangeably. This is also in the case of referring to items like this: dit/dat boek, die/deze boeken (this/that book, these/those books). But when in English you would say "this/that/those/these one(s)", there is more flexibility. So following your example, all these things would be correct: Dat heeft ze nog niet (e.g. when somebody else holds the item) Dit heeft ze nog niet (e.g. when you hold the item) Die heeft ze nog niet (e.g. when somebody else holds the item) Deze heeft ze nog niet (e.g. when you hold the item) You would expect that the article and the plural matter for which one you should use, but that is not the case!

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When referring to 'de boeken' you will have to refer to it as DIE because it's a 'de' word in this form. Your first question is difficult to answer for me since I'm not a Dutch teacher. They would probably know how to answer this. I would personally in that specific sentence always use DIE. However when you have a sentence like this: Het boek, ____ ik gelezen heb. In this situation you away use DAT, like you would naturally do.