the question is literally "have they a book?" you don't need the "do" in these sorts of questions

You don't use do in french like you do in english.

Well you should have at least guessed it because of the times that example has been shown. Like, for example, the time when they asked for the English translation of the French sentence "Ont - Ils un serpent?" and you had to reply with the English translation, "Have they a snake?", or "Do they have a snake?" Ring a bell?

I agree. They should figure out a better way to introduce concepts, like how to arrange a question.

Indeed, "il sont" does not exist in French, and "ils ont" is used frequently (just not in this particular example), but just to help clarify the phonetic question further: In French "ils ont" (they have) and "ils sont" (they are) are indeed phonetically different, as "ils ont" is pronounced with a liaison and "ils sont" is not. In liaisons, "s" is pronounced like a "z." As such, "ils ont" is pronounced something like "eelzohn," whereas "ils sont" is pronounced like "eels sohn." Tricky, I know! But just as you likely have little trouble distinguishing "race" and "raze" in English, thanks to both the subtle phonetic difference and the context, with enough exposure, this shouldn't be too tricky.

But "Il sont" doesn't exist. The corect form is "il est" (he is). I didn't understand very well your question.

No. Questions in French can be phrased many ways.

You could say

Ils ont un livre?

Ont-ils un livre?

Est-ce qu'ils ont un livre?

French speakers can hear the difference between "ils sont" and "ils ont", they changing of the verb order affects the formality of the question (I think.)

It came from avoir conjugate for Ils / Elles.

It can be 'Ils ont un livre?" and also "Est-ce qu'ils ont un livre?" I think.

No, beacuse "font" means "to do", as a verb (as in "do your homework) , and not as an auxiliary for questions. If you are an English speaker it's pretty easy to make questions, you need the auxiliary "est-ce que" which is equivalent to the auxiliary "do" (so the answer is "est-ce qu'ils ont un livre?" = do they have a book? )

Hyphens are used between the subject and the verb when there is an inversion (i.e., when the usual order of a subject followed by a verb is flipped to a verb followed by a subject). Using an inversion is one of the ways to ask questions in French (particularly in formal contexts). In this case, "ils" is the subject and "ont" is the verb, and "ils ont" (which means "they have") has been inverted to form "ont-ils?" (which means "do they have?").

In fact, a similar inversion (sans the hyphen) works in English as well, "They have " becomes a question if we swap the order and say "have they?" It's just less commonly used.

(Note that questions are not the only instances where you will encounter inversions, and inversions are not the only place where hyphens are used. You'll encounter more as you get into more advanced French. Just a heads up!)

That means, Do you have a book?

What you are trying to say is "Do they have a book?"

Furthermore 'ont' is the 'they' conjugate of 'avoir,' which means 'have.'

The hypen (-) and reversal of 'ils' and 'ont' implies a question.

Like waphle states above it's like English when you ask "have they a book?" so "ont-ils un livre"

you don't translate "do" into french, you just ask "they have a book?" - "ils/elles ont un livre?"

In English, we only have two verb conjugations for "two have" in the present tense – ”has" or "have." But in French, we have six for the present tense, one for each subject type.

• "Ont" is used for the third person plural ("ils ont" or "elles ont," – the equivalents of "they have"), as in this example.
• "Avez" is used for the second person plural or informal ("vous avez" – the formal or plural equivalent of "you have"). As such, to answer your question, you would say "vous avez un chat."
• The other present tense conjugations are "j'ai" for "I have," "tu as" for "you have" in the informal, "il/elle a" for "he/she has," and "nous avons" for "we have."

Hope that clarifies! Let me know if you have any other questions.

As long as there is at least one male (or, when talking about objects, at least one masculine noun) in the group, you would use "ils." You use "elles" only when the group has only females or feminine nouns.

There are multiple ways of asking questions in French. The way you've mentioned is one common one – adding "est-ce que" to the beginning of a regular statement. Another common way is the one used here – inversion, where the usual subject-verb order is flipped. In this case, "ils" is the subject and "ont" is the verb, and "ils ont" ("they have") has been inverted to form "ont-ils?" ("do they have?").