Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil; Heb 2:14
Is that, the death, that the sin of Adam brought to all men?
That's actually a complicated question, because we have two deaths we must be aware of in Scripture: physical, and spiritual.
In large part physical death is the primary penalty for Adam's sin. He lost access to the Tree of Life, which we presume contributed to continued physical existence (it never has nor ever will bestow eternal life, only God can do that through immersing believers into Himself). If you look at the Law, the penalty was physical death, not spiritual. If you look at the provision of vicarious death (animal sacrifice), all that granted was extended physical life.
Secondly, I don't think we can attribute full power of death to Satan, but rather he is a cause of death in man, because just as he caused Adam to sin (and therefore die), his intent is to destroy men whenever he can. God is Sovereign, and that means over both life and death (as seen in the example of Job, Satan was forbidden to kill him (physically)).
Third, in regards to spiritual death, or, Eternal Judgment, the basis of punishment is not because we descend from Adam, but because we...sin. Every man will be judged according to the sin he commits, as shown in passages such as Ezekiel 18 (which is a physical context), Hebrews 10:26-28, and 2 Peter 2.
So the death in view would first be physical death. That this extends to eternal judgment can be seen, but I don't think we can dogmatically assert that everyone put to death in violation of the Law will undergo Eternal Separation, because even among Christians today the (physical) death penalty still exists. God can take the life of a Christian who is unrepentant in sin. This is seen in Ananias and Sapphira (and of course this applies assuming they were born again believers) and those who died because of partaking of Communion unworthily.
Why did God put the man in the garden he had planted where the devil happened to be.
Show me where Satan "was in the Garden" when God created it.
What we are told is that it was the Serpent, and based on New Testament revelation we know that it was Satan behind what took place. I look at this as more of an instance of possession rather than the serpent was actually Satan, or at least, think that is more likely (because the serpent is cursed). Secondly, I think we also consider the fact that Satan is said in a couple places to be one who roams the earth, which means Satan was a visitor to the Garden for his evil purpose, not a resident.
I think it a mistake to consider Satan as being part of Creation. There is no mention of Angels being part of Creation, other than as observers.
Was the purpose of putting him there to test the man or for some purpose relative to the mission of the Son of God to be manifested as a man, flesh and blood?
God didn't need to test Adam, He knew he would sin, and this before He even created the heavens and the earth.
Angels and demons are spirits, not gods, not men. The heavens and the earth were created for man, not Angels. Hell was created for Satan and his demons, and we cannot say for sure when that took place, but, it likely took place prior to the creation of the heavens and the earth.
You said the sinful devil already existed before the man was created in the image of God, therefore, did sin have to take place in order that; through death he might destroy him that had the power of death, that is, the devil, to take place?
From a perspective dealing with man, perhaps. From a perspective dealing with fallen Angels, not really. God could have destroyed Satan and his cohorts at any time, and still can. Apparently they serve a purpose for now, but we can look at the Millennial Kingdom to see that Satan need not be on earth in order for man to sin. It might be viewed as similar to boot camp, which has obstacle courses, physical training, and drill instructors (who I am sure more than a few have likened to demons, lol).
But again, God knew in advance that Adam would sin, and that death would come to all men, and that men would need to be reconciled to Himself. I think Reconciliation will place man in a higher state than Adam was when he was created, because God immerses believers in Himself, and will give them bodies suited to everlasting existence, which Adam was not created with. At least, that is how I see it. If Adam had not sinned, it is likely he would have continued to live forever, having access to the Tree of Life. But God knew that the result of man falling and being reconciled to Himself would produce a creation far greater than that originally designed.
That is the Body of Christ, the Church.
God bless.