If the one born in Bethlehem was ‘a creature’ (as says Arius) and yet did not sin, then why was the first humanity (Adam) not so created?

Did Arius state that Jesus was a mere human being? No person that knows anything about Arius would say such a thing. Arius wrote that the Son was “begotten timelessly by the Father … before aeons … begotten timelessly before everything” (RPC Hanson - The Search for the Christian Doctrine of God - The Arian Controversy 318-381, page 8). “He who has begotten the only-begotten Son … through whom also he made the aeons and everything” (page 7).

Why did God not create Adam without the ability to sin? Because God created mankind with the freedom to choose between good and evil. To create people without the ability to do evil is to create pre-programmed robots. But God created something much, much better.

Was Jesus able to sin? I say He was, otherwise His whole mission and Satan's efforts to get Him to sin were a farce.

But then, why did Jesus not Sin? The purpose of His mission to earth was to show that the Son of God would not sin, even when tempted to the utmost. It was a test. Satan said He would sin. The Son was willing to become a human being, to be tested and to suffer all possible loss. His purpose was to validate the credibility of the Saviour, without which no sinner can be saved. Jesus did not sin because the Son of God is able to disobey God but He never will. That was shown at the Cross.

See: In the book of Revelation, why did Jesus have to die?

Answers here must necessarily be speculative because so little survives from Arius' own pen, and what we have is filtered through the minds of his opponents. That said, the answer is probably simple: Adam misused his free will and failed to keep God's commandment; Jesus did not.

Fault with the creator?

It is not fair to say that Arius "found fault with the creator." It is true to say that the Arian view implies that God's first attempt (with Adam and Eve) to create a true humanity did not come to fruition. Either way, an Arian could counter the idea that Arius found fault with God by referring to examples from providential history in which God's plan seems at first to have failed but later succeeds. For example, in 1 Kings 11:36 God promised "David my servant will always have a lamp before me in Jerusalem." But when the kings of Judah failed, God promised to send the messiah to restore David's kingdom. As a result, Jews expected the messiah to re-establish the throne of David, but this did not occur. Christians of nearly all types explain that this was not God's fault, because the throne of David would be established at Christ's second coming. Similarly, and Arian could argue that it was not God's fault that Adam sinned, necessitating a new Adam to arrive to restore Adam's fall.

Predestination

Underlying this problem are the issues of Original Sin and predestination. We do not know Arius' view on this. But we can speculate that Arius' view was more Pelagian (although neither Augustine nor Pelagius was on the scene yet), believing that God had not predestined Jesus' obedience any more than he had predestined Adam's. If so, then Jesus could have sinned as Adam did, but he aligned his will with that of the Father, thus maintaining his status as God's Son. To the objection that his is a form of works-righteousness, an Arian might respond that we are not saved by works, but Jesus did save us by his works, if we have faith in his atoning sacrifice. This does imply, however, that if Jesus had sinned in a way that compromised his providential status, he would be disqualified from Sonship. However, we do not have enough information on the Arian doctrine to know this for certain.

Merely another creature?

Finally, it is also inaccurate to say that Arius thought of Christ as "merely another creature." He affirmed the Son to have pre-existed with the Father as the first of God's creations after God created the Word. Jesus was an incarnation of the pre-existing Son, not a mere human being. A letter of Arius summarized [whether accurately or not] by Eusebius of Nicomedia states:

The Son... was made on our account, in order that God might create us by him, as by an instrument; nor would he ever have existed, unless God had wished to create us.

Did this apply also to Adam, in Arius' though? Not enough of Arius' actual teachings have survived for us to know. The same may be said of some of the other issues raised in the OP. But as far as the main question goes, a simple answer is possible: Arius might answer that both Adam and Jesus were created with free will, either to sin or not. Adam and Eve did sin. Jesus did not, at least not in a way that disqualified him from Sonship.