Almost every small Jewish child learns the Mah Nishtanah sometimes even in multiple languages the questions remains is that the question remains. Where in the Haggadah are the four questions answered (please do not tell me "Ha Lach Mianya" and if you do please tell me how it does) where in the Haggadah do we find direct answers to the questions asked? any article or your own answer would be appreciated!
I'll deal with one potential aspect of your question, and hopefully others will be able to add more: to what extent are the questions in Mah Nishtanah answered within the text of Mah Nishtanah itself? This issue is discussed at length by Prof. Richard C. Steiner of Yeshiva University, in an article titled, "On the Original Structure and Meaning of Mah Nishtannah and the History of its Reinterpretation" (JSIJ 7 , 163-204). The article can be read online here, and I summarise it below.
There are at least three different ways of construing the number of questions in the Mah Nishtanah, at least one of which provides answers. The differences in interpretation boil down to three different ways of construing the word mah (מה), and three different ways of construing the particle she- (ש). Those different interpretations are as follows:
1) Mah (מה) = "What?"; she- (ש) = "[such] that".
"What differentiates this night from all other nights, such that [examples A, B, C, D]?"
This interpretation of the two lexemes (mah and she-) has great precedent, and elicits a reading of the text in which there is a single question: what is it about this night to have produced these four differences between it and all others?
2) Mah (מה) = "Why?"; she- (ש) = "for".
"Why is this night different from all other nights? For, [examples A? B? C? D?]"
This is the best attested interpretation of the text, although it too can be understood in three different ways:
- Four questions: why is this night different in respect of example A? In respect of example B? In respect of example C? etc;
- Five questions: Why is this night different from all other nights? Why do we do example A? Why do we do example B? etc;
- One question, and four answers: Why is this night different from all other nights? Because of example A, because of example B, because of example C and because of example D.
3) Mah (מה) = "How!"; she- (ש) = "for" (idiomatically, "why")
"How different this night is from all other nights! Why, [examples A! B! C! D!]"
This interpretation also has some precedent, though it yields a reading of the text in which there are no questions, being a rhetorical assertion only, and therefore one in which it also requires no answers.
The only construals of the text that require an answer are those found in interpretation 1 (a single question), interpretation 2.1 (four questions) and interpretation 2.2 (five questions). Where the first (1) asks about the general nature of the evening, and the second (2.1) about the specific things that we are doing, the third (2.2) combines them both together. You might suppose that the entirety of the haggadah is an answer to that first question, while the second (why do we do examples A, B, C and D?) is answered more specifically at various junctures within it.
Fascinatingly, the 1609 Venetian Haggadah was printed with three different translations: Yiddish, Judeo-Italian and Judeo-Spanish. All three of these translations rendered the mah (מה) in Mah Nishtanah differently:
Yiddish: וואז ("What?"); Judeo-Italian: פַיר קַי ("Why?"); Judeo-Spanish: קואנטו ("How!").
I encourage you to read Prof. Steiner's full article, which is considerably more thorough than what I have presented here.
The Maharal in Gevuros Hashem Ch. 52 suggests two answers to this question:
דודאי התשובה הוא בסוף המאמר שמשיב על פסח מצה ומרור כאשר מגיע לשם... וכן על שאנו מסובין משיב בכל דור ודור חייב אדם לראות את עצמו כאלו הוא יצא ממצרים וכו' ומפני שיראה עצמו כאילו יצא ממצרים יש לעשות הסבה
The answer is at the end in the description of the Pesach sacrifice, matzah, and marror, when he gets there... and that which we lean is answered in the paragraph in which we declare that in every generation one must see one's self as if he himself left Egypt, and therefore he should lean
כי מה נשתנה שאלת חכם... ויודע הוא זה... אלא ששואל מה ענין זה לנו כי מה קרה לנו ... ומתרץ עבדים היינו לפרעה
Mah Nishtana is the question of a scholar... and he understands the meaning of all of these things... rather he is asking what does this have to do with us, and what happened to us... and the answer is "we were slaves to Pharaoh etc."
I skipped the supports that he brings to his idea, but you can see it here.
Rabbi Yosef Yitzchok Katz in a sefer called Haggadah KeHalachah (p. 282) explains that all the questions are answered in the first paragraph, as subsequently expounded in the Haggadah.
ויוציאנו ה' משם - G-d took us out from there, which was in a way that there was no time for the dough to rise, so we only eat Matzah.
עבדים היינו - We were slaves, and the Egyptians embittered our lives during that slavery, so we eat bitter herbs.
ביד חזקה - With a strong hand, meaning that we are free today, so we lean like free people.
Regarding dipping he says that the only questions the Haggadah answers are those that address the specific practices for the seder night, not those that the child was taught to say but that he didn't observe. The only dipping he observed so far was Karpas which was only so that he should ask.
[Presumibly he means that the Matza and Morror he observes with Yachatz and on the Seder plate.]
He then brings the Abarbanel's answer (Zevach Pesach on Avadim HaYinu) that the answer is that tonight we are making a remembrance for two times in the life of our forefathers in Egypt. At the beginning of the night, we were slaves, therefore we do remembrances of slavery - the Matzah and the Morror. Then Hashem took us out, so we dip twice and lean while eating to commemorate the freedom.
The first two questions (assuming that we consider the 1st question to be the one about matzah, and the 2nd about maror) are answered quite directly just after the "Rabban Gamliel" section/ It explains why we eat matzah; another paragraph why we eat marror.
Offhand, I don't know where the hagadah answers directly the last 2 questions about dipping & reclining.
Dipping can be associated with the splitting of the sea (in Hallel), while reclining can be associated with the four cups of wine.