Learn Russian: Разве это твоя книга?

Разве is a special question particle that shows surprise, doubt, or disbelief. While a standard question just asks for information, starting with разве changes the meaning to "Is it really true that...?" or "Can it be that...?"

Since книга (book) is feminine, why do we use the neutral это instead of the feminine эта?

When you use "this" as a standalone subject to mean "This is a [noun]", you always use the neutral это, regardless of the noun's gender. You only use the feminine эта when it attaches directly to the noun to mean "this specific [noun]", like in Эта книга твоя? (Is this book yours?).

Why is there no verb for "is" in this sentence?

In Russian, the present tense of the verb "to be" (am, is, are) is almost always dropped. To say "This is your book", you simply put the words side by side: Это твоя книга (literally "This your book").

Can I use неужели instead of разве here?

Yes! Both are used to ask questions with a sense of surprise. The difference is just how strong the feeling is. Неужели expresses much stronger shock or disbelief ("Is it really possible?!"), while разве is a bit milder.