One of the other lessons said there are certain contexts where "des" becomes "de" even for plurals. I forget when, but it's either showed up in the past or will show up in the future, depending on when Duo decides to present it. Also take a look at
I am coming to think (and maybe this is also the answer to my question about des) that "livre de recettes" is a phrase that means "recipe book" and it just is how it is. If a French speaker asked me why we don't call it a "recipes book" or a "photos album" I couldn't really tell them; that is just how English describes books. It's a specific rule we have for those kinds of items. In that case maybe the answer to your question is that "livre de recettes" is a common phrase and "livre de recette" isn't?
I think there is some logic there, though. In English, when we use a noun as an adjective (as in "recipe book" or "photo album"), we use the singular form. When we use the possessive, we use singular or plural as determined by the context (the photo's frame, women's hats). I can't address the French situation, though!
No, I'm pretty sure you can't say "mon recettes livre." In English, we can use a noun (recipe) to modify another noun (book) directly - what kind of book? A recipe book. (We're basically using the noun as an adjective.) German can do that too, though differently. But not all languages can. In Spanish if you want to use two nouns together you generally have to explicitly connect the two using "de" (book OF recipes). The same seems to be true in French.
When doing French to English "recettes" is shown as either "receipts" or "recipes" without explanation. So when going from French to English for "C'est mon livre de recettes" I thought "This is my receipt book" to be an acceptable answer. It was marked wrong.
I'm an accountant so would naturally think of receipts rather than recipes. Plus the French word is more of a phonetic match!