Translation:This is the first page of my new book.
why can't it translate to "This is the first page in my book" instead of "of my book"?
I agree, I don't think there's sufficient difference between the two versions not to accept.
Is it possible to tell from this sentence whether "my new book" is a book that I'm writing or a book that I'm reading?
No, but with probability close to 100% this will mean "a book that I'm writing", especially in this context. To indicate that this is a book that you're reading, you need to rebuild the sentence: "Это первая страница книги, которую я недавно купил." (This is the first page of a book I bought recently.)
Thank you. I suspected that one or the other would require a different sentence but I wasn't sure which.
It seems that the word "новая" is what adds that "is being written by me" sense in the first place. Without it ("Это моя книга"), this is just a book, which I own.
When is эта used? I thought it would be here because страница is feminine, but apparently not
You use это instead of этот/эта/эти when its the subject of a sentence. So if the sentence was "This page is the first in my new book" (correct me if im wrong)"Эта страница - первая моей новой книги"
Моей is used here because "book" (книга) is feminine.
Моего is used with masculine or neuter (singular) nouns in genitive.
(Моих would be used for genitive plural.)