It is hard for a native English speaker to know what "This book is not ending" actually means. It is an unnatural expression that would certainly provoke a request for explanation. Does it mean 'it is as if this book never ends', i.e. a complaint about a long book?. If so, I would joke "This book is never-ending". Or does it mean something totally different?
You pinpoint one of the weak spots in Duolingo. I often struggle with deciding what I would say in the real world and what I think that Duolingo would accept. This exercise is a good example as I would never say "this book is not ending". Nevertheless, that is what I wrote.
I think this should be corrected, because there is no such a thing like that... And for me it is clear that the meaning of the Turkish setence is about "a book that is endless or does not have an end." So the correct answer need to be choose between "This book is endless." or "This book does not end." I never saw "is does not" to refer a 3SG in a English sentence before.
This sentence is an example of the continuous tense being used where you would almost always use "will do sth" in English. Turkish speakers use this often (almost exclusively) to promise things they will do. e.g. I will take care of the kids, you can go shopping at ease, don't worry about the kids: Çocuklara ben bakarım, sen rahatça alışverişe çıkabilirsin, aklın çocuklarda kalmasın.
Turkish people will also almost never use the usual "geniş zaman", i.e. "-er" to mean I cook, I play, I go outside etc. ; the natural-sounding Turkish equivalents for those would be yemek pişiriyorum (her gün yemek pişiriyorum: I cook every day), oyun oynuyorum (hafta sonları arkadaşlarımla parkta top oynuyorum: I play ball with my friends in the park on the weekends) and dışarı çıkıyorum (I go out whenever I feel bored: Canım sıkıldığında dışarı çıkıyorum)
The "geniş zaman" is really what it sounds like: it's wide. It's for a longer period of time than just every week or every year. It's not defined, it could be near future, but it could also be 2 years later from now. That's why a promise given in this way will be as trustworthy as given in English with "I will do ... sometime" would be.