Although this set of questions calls for a personal response, the following points should help you to answer. First, Turtles All the Way Down is generally regarded as being exceptionally well-written at the sentence level, with many memorable phrases. However, readers may find some of the events in the book difficult to believe. The teenage sleuth pursuing the missing billionaire is unlikely enough, but when the billionaire's son attempts to pay her off with $100,000 which his father keeps casually stashed around the house, this seems even less believable. The characterization, however, is generally credible, and the book is certainly original, particularly in its incorporation of literary references, psychology, and philosophy.
Aza's unusual way of viewing the world, and her interactions with her therapist and other intelligent characters, allows the literary and philosophical elements to be relatively unobtrusive, though the result is still very much a novel of ideas. You will probably have your own views about the most outstanding sentences and passages of writing in the book, but here are a few striking examples to consider, all of which are thought-provoking and strongly expressed:
The problem with happy endings is that they're either not really happy, or not really endings, you know? In real life, some things get better and some things get worse. And then eventually you die.
You're both the fire and the water that extinguishes it. You're the narrator, the protagonist, and the sidekick. You're the storyteller and the story told. You are somebody's something, but you are also your you.
Our hearts were broken in the same places. That's something like love, but maybe not quite the thing itself.
I would never slay the dragon, because the dragon was also me.
I couldn't make myself happy, but I could make people around me miserable.
There are many more instances of both short, pithy phrases and long expository passages which show the author's skill. Green's greatest strength is at the level of the sentence, rather than in tight plotting, and some readers may be frustrated by the inconclusive ending. However, the first of the quotations above makes Green's thoughts on happy endings quite clear.