does the argument between Adam(PBUH) and Moses(PBUH) make it that Adam(PBUH) had no free will?

Question

in the following Hadith Moses(PBUH) blame Adam(PBUH) for eating from the tree but Adam(PBUH) responds that it wasn't his fault and Allah(SWT) pre-ordained it for him and he is not to be blamed, and then the prophet(PBUH) said: "This is how Adam came the better of Moses and Adam came the better of Moses." so this mean that Adam(PBUH) was right and he had no free will at all!

Abu Huraira reported Allah's Messenger ﷺ as saying: There was argument between Adam and Moses. Moses said to Adam: You are our father. You did us harm and caused us to get out of Paradise. Adam said to him: You are Moses. Allah selected you (for direct conversation with you) and wrote with His own Hand the Book (Torah) for you. Despite this you blame me for an act which Allah had ordained for me forty years before He created me. Allah's Apostle ﷺ said:. This is how Adam came the better of Moses and Adam came the better of Moses.

(Sahih Muslim 2652a)

Answer 1

This hadith was compiled in many hadith sources (ibn Hajar counted 10 routes to abu Hurrairah in his fath al-Bary -see here in Arabic-) among them in both Sahihs:

• Sahih al-Bukhari
  in the book of Tawheed via ibn Shihab az-Zuhri from Hamid ibn 'Abdarrahman, in the book of destiny via Sufyan ibn 'Uyyanah from Tawoos, in the book of Prophets via ibn Shihab az-zuhri from Hamid ibn 'Abarrahman (again but with differences in the chain), in the book of Tafsir via ibn Sireen and via abu Salamah

• Sahih Muslim
  in the book of destiny via imam Sufyan ibn 'Uyyana from 'Amr ibn Dinar, via imam Malik from abu az-Zinad from ibn Hurmuz (al-A'raj), via al-Harith ibn abi Dibab from ibn Hurmuz, via ibn Shihab az-Zuhri from Hamid ibn 'Abdarrahman, via Yahya ibn Kathir from abu Salamah, via Humam ibn Munabbih via Muhammad ibn Sireen

Now let's go back to your inquiry.

First of all we need to understand the hadith well:

• What is Musa's () point?
  Musa () "accused" Adam () to have misled the people, and caused them to get out of paradise (Jannah). What is the truth about this accusation?
  The truth is that Adam's() sin caused him and his wife to get out of paradise and therefore his offspring too.
  But did Adam () know that a sin would cause him to be expelled from Jannah?
  Or was this knowledge by Allah () and Allah has decided long before Adam's creation that if Adam () will sin he would be expelled?
  The question here is whether Allah () has created the deeds and acts of his creation or is every creation the origin of its acts and deeds?
  The Qadari's consider the humans or the creation as the origin of their acts and deeds therefore they would say else why would Allah () order or prohibit.
  However Allah says refuting the claim that somebody else than Allah can create or create an act:

• That is Allah , your Lord; there is no deity except Him, the Creator of all things, so worship Him. And He is Disposer of all things. (6:102)

• While Allah created you and that which you do?" (37:96)

While Allah said via Musa in the qur'an:

...This is not but Your trial by which You send astray whom You will and guide whom You will....(7:155)

Which means that Allah() created us and gave us the means to do things or to leave them so he showed us good and evil and he gave us the means to act upon our choice. People who don't follow Allah's guidance therefore will go astray. So the view of ahl-as-Sunnah wal Jama'a on this topic is that creation of things is by Allah, while earning from these things is given to His creation. (For more details refer to the commentary of ibn Battal al-Maliki on Sahih al-Bukhari -see here and the following pages in Arabic-)

2. How to understand Adam's () answer?
   The Jahamiyah however used the statement that Allah ordained Adam () things before his creation to support their claim that Adam () had no free-will.
   This is also wrong as people don't commit sin without an intention, will or desire.

TO BE ELABORATED

3. Why Adam () had the stronger argument?
   Because Allah forgave Adam's() sin Allah said:

Then Adam received from his Lord [some] words, and He accepted his repentance. Indeed, it is He who is the Accepting of repentance, the Merciful. (2:37)

and further He informed Musa () in the Torah about this and about the fact that He already planed for Adam things (40 years according some ahadith) before his creation, as Allah said:

nd [mention, O Muhammad], when your Lord said to the angels, "Indeed, I will make upon the earth a successive authority." ... (2:30)

Therefore Musa() had no point to accuse Adam() for this mistake or misdeed.

Answer 2

Yes.

But infact, it is more like Predestination than no free-will.

The boy that Al-Khidr killed was destined to be a disbeliever the day he was created.

~ (Tirmidi 3150, Abu Dawud 4705)

Abdullah (b. Mas'ud) reported that Allah's Messenger (may peace be upon him) who is the most truthful (of the human beings) and his being truthful (is a fact) said: Verily your creation is on this wise. The constituents of one of you are collected for forty days in his mother's womb in the form of blood, after which it becomes a clot of blood in another period of forty days. Then it becomes a lump of flesh and forty days later Allah sends His angel to it with instructions concerning four things, so the angel writes down his livelihood, his death, his deeds, his fortune and misfortune. By Him, besides Whom there is no god, that one amongst you acts like the people deserving Paradise until between him and Paradise there remains but the distance of a cubit, when suddenly the writing of destiny overcomes him and he begins to act like the denizens of Hell and thus enters Hell, and another one acts in the way of the denizens of Hell, until there remains between him and Hell a distance of a cubit that the writing of destiny overcomes him and then he begins to act like the people of Paradise and enters Paradise…

~ (Muslim 6390)

Hudhaifa b. Usaid reported directly from Allah's Messenger (may peace be upon him) that lie said: When the drop of (semen) remains in the womb for forty or fifty (days) or forty nights, the angel comes and says : My Lord, will he be good or evil ? And both these things would be written. Then the angel says: My Lord, would he be male or female ? And both these things are written. And his deeds and actions, his death, his livelihood; these are also recorded. Then his document of destiny is rolled and there is no addition to and subtraction from it.

~ (Muslim 2644)

Anas b. Malik reported directly from Allah's Messenger (may peace be upon him) that he said: Allah, the Exalted and Glorious, has appointed an angel as the caretaker of the womb, and he would say: My Lord, it is now a drop of semen; my Lord, It is now a clot of blood; my Lord, it has now become a lump of flesh, and when Allah decides to give it a final shape, the angel says: My Lord, would it be male or female or would he be an evil or a good person? What about his livelihood and his age? And it is all written as he is in the womb of his mother.

~ (Muslim 2646)

Ali reported: We were at a funeral in the graveyard of Gharqad that Allah's Messenger (may peace be upon him) came to us and we sat around him. He had a stick with him. He lowered his head and began to scratch the earth with his stick, and then raided: There is not one amongst you whom a seat in Paradise or Hell has not been allotted and about whom it has not been written down whether he would be an evil person or a blessed person. A person said: Allah's Messenger, should we not then depend upon our destiny and abandon our deeds? Thereupon he said: Acts of everyone will be facilitated in, that which has been created for him so that whoever belongs to the com. pany of the blessed will have good works made easier for him and whoever belongs to the unfortunate ones will have evil acts made easier for him. He then recited this verse (from the Qur'an): "Then, who gives to the needy and guardsagainst evil and accepts the excellent (the truth of Islam and the path of righteousness it prescribes), We shall make easy for him the easy end and who is miserly and considers himself above need, We shall make easy for him the dificult end.

~ Muslim 2647a

Answer 3

Adam (PBUH) repented and asked for forgiveness and Allah forgave him. So Adam (PBUH) is not blameworthy and that might be the reason Adam (PBUH) is telling Musa (PBUH) why you are blaming me. And Moses (PBUH) was blaming Adam (PBUH) for the consequence, and he is the reason we are on the earth. But that argument was weak as Allah knows the future and what will happen and he wrote our fate already. And Allah already had a pre-plan to send us to the earth to test us and worship him alone. So blaming Adam (PBUH) was weaker in the argument. But for the sins, a person is blameworthy for his own sins. But not for other actions for which he/she had repented or the actions/things that happen around us usually like Adam (PBUH)'s descending from heaven to earth.

Secondly, already written our fate doesn't mean we don't have free will. Allah knows the future and what we will do, and if he writes all our future before our creation, that doesn't mean we don't have free will and we are not in a test.

For example, if I am a teacher and I know among my students who will pass the test and who won't, and if I write down the result, and then take a test, does that mean I didn't give them free will? Also, Does that mean I won't take the exam? Otherwise, the student who failed the exam will protest and call the teacher unjust.