I think one of the clearest scripture is in Col 2:15, that's what' I meant by defeated.
And rightly so; let's look close:
Colossians 2:13b-16a
He has made alive together with Him, having forgiven you all trespasses, 14 having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross. 15 Having disarmed principalities and powers, He made a public spectacle of them, triumphing over them in it.
16 So let no one judge you....
It is about what Jesus did on the cross, I'm sure we'd agree. Because of what Jesus did we are alive, forgiven, no requirement of justice remaining against us. In context, by doing this, Jesus has disarmed the principalities and powers. He publicly showed them for what they were: users and abusers. But because the accusation against us is wiped clean, leaving no accusation to be made, the enemies are disarmed....they have no weapon to attack with (unless we once again turn from God's will in our lives for us and embrace the curse, thus opening a door for the enemy to enter and lie to us about our position in Christ). In other words, the enemy has not been changed, but his ability to accuse us has been drained and dried up. Stay under God's wing, stay in His blessing, and the enemy cannot touch you.
You know Blessed Man, I'll prefer to use the titles of scriptures gives instead of my definition of god.
First and foremost everyone should learn from what you say here. Too many times we wonder ABOUT scripture and go off and create a man-made explanation for the 'why' and 'what' of scripture without either letting it answer the question, or realizing that for whatever reason the answer was not explicitly provided by God to man. It's ok to ponder, but not to create theologies from the silence.
I think it's reasonable that "god of this world" is able to promises the world to Jesus in the wilderness.
Simply because Jesus did not deny Satan's statement does not mean that He agreed with it. To take either stand from this verse is preaching from silence. Jesus simply replied about Who to serve.
Luke 4:5-8 (NKJV)
5 Then the devil, taking Him up on a high mountain, showed Him all the kingdoms of the world in a moment of time. 6 And the devil said to Him, “All this authority I will give You, and their glory; for this has been delivered to me, and I give it to whomever I wish. 7 Therefore, if You will worship before me, all will be Yours.”
8 And Jesus answered and said to him, “Get behind Me, Satan! For it is written, ‘You shall worship the Lord your God, and Him only you shall serve.’ ”
NASB v6: And the devil said to Him, "I will give You all this domain and its glory; for it has been handed over to me, and I give it to whomever I wish.
The Greek word is
exousia. It literally means ability, privilege, influence, jurisdiction, power, authority. It has a 'flavor' of being legal -- in fact it's root is from
exesti, which means to be lawful.
We see this same word usage in many verses:
- For he taught them as one having authority... Matt 7:29
- For I am a man under authority... Matt 8:9
- ...his twelve disciples, he gave them power over unclean spirits... Matt 10:1
- I give you power over serpents and scorpions.... Luke 10:19
- [Pilate] knowest thou not that i have power to crucify... John 19:10
- ...but has power over his own will... 1 Cor 7:37
- they worshipped the dragon which gave power to the beast ... Rev 13:4
So we have Jesus' authority to teach, a soldier's authority to lead, our authority over the enemy, man's power to judge another unto death, our control of our will, and the enemies power to wage war.
Bear with me here, this is going somewhere

So now let's take a look at these verses:
Psalm 82:6
I said, “You are gods,
And all of you are children of the Most High.
and
John 10:34
The Jews answered Him, saying, “For a good work we do not stone You, but for blasphemy, and because You, being a Man, make Yourself God.”
34 Jesus answered them, “Is it not written in your law, ‘I said, “You are gods”’? 35 If He called them gods, to whom the word of God came (and the Scripture cannot be broken), 36 do you say of Him whom the Father sanctified and sent into the world, ‘You are blaspheming,’ because I said, ‘I am the Son of God’?
In Psalm 82 the word is
elohim. It is the same word that renders God (as in Almighty God). Here God uses it to refer to men. This is not a deification of men, but has a meaning that is very significant here, which I'll get to.
In John 10:34 the word is
theos. It is the same word that renders God (as in Almighty God). Here Jesus uses it to refer to men. Again, this is not a deification of men....
This word in the Old and the New Testaments, when ascribed to men, means rulers and judges. It is someone who has power and authority over another group, such authority having a form of legal merit.
Back to the word
elohim. This word also includes angels. Of which Lucifer is one. Thus, god of this world (2 Cor 4:4). It means magistrate or prince. Thus, prince of the power of the air (Eph 2:2). It means ruler. Thus, ruler of this world (John 12:31).
Thus:
He's also called prince of this world. He is also called ruler of this world. All these titles presupposes some sort of power and even authority.
Satan is part of the elohim, albeit a fallen part. He became prideful and was cast out of heaven, but we see him in Job entering the throne room as "the sons of God came to present themselves before the Lord, and Satan also came among them." (Job 1:6)
Satan acquired dominion in this earth. Whether that acquisition came as a result of the fall or was an assignment from the beginning of creation is not clear. His dominion, though, is spoken of in the passages that you quote and others.
And as Psalm 82 -- and Jesus echoing that in John 10 -- tells us, man is also a part of the elohim: the rulers and judges.
Was anything transferred to Satan through Adam's fall? I'd think so. But I'm not too sure about technicalities though.
Well, we (especially in WoF) attribute a power transfer in the fall. But scripture is not clear of the
transfer. Satan obviously had a right to be in the garden (for if God is omniscient and omnipresent, then certainly He knew the devil was there). Satan had a right to talk to man. But he couldn't MAKE Eve eat that fruit -- he could only deceive her and suggest that she eat it. When she did, and Adam in her wake, man disobeyed God's direct command and sinned: of their own free will.
The real question is "what does Satan have dominion over?"
Colossians 1:13
He has delivered us from the power of darkness and conveyed us into the kingdom of the Son of His love...
1 John 5:19
We know that we are of God, and the whole world lies under the sway of the wicked one.
Ephesians 2:2
in which you once walked according to the course of this world, according to the prince of the power of the air, the spirit who now works in the sons of disobedience,
2 Timothy 2:26
and that they may come to their senses and escape the snare of the devil, having been taken captive by him to do his will.
We have been delivered
from Satan's power (his power was not taken away!). We are of God, but the world is under Satan's dominion. We once walked under Satan's domain, and the unsaved still do. And we pray that the unsaved will, by their own free will, escape the devil's dominion and come to Christ.
But if Satan was in the garden and got Adam and Eve to come under his sway: then he
already had such a domain
PRIOR to the fall. One could argue that it was created as a result of the fall, and I would not have much issue with that. Once reason I tend toward a "prior" belief is "
tohu bohu":
Genesis 1:1-2
In the beginning God created the heavens and the earth. 2 The earth was without form, and void; and darkness was on the face of the deep. And the Spirit of God was hovering over the face of the waters.
Isaiah 45:18
For thus says the Lord,
Who created the heavens,
Who is God,
Who formed the earth and made it,
Who has established it,
Who did not create it in vain,
Who formed it to be inhabited:
“I am the Lord, and there is no other.
God's creation is perfect (v1). In verse 2 it suddenly is "without form, and void" (Heb:
tohu bohu). Tohu means chaos; bohu means void, vacant. In Isaiah 45:18 we are told that God did not create it in vain (tohu -- literally chaos). Something happened to the earth PRIOR to the creation of man. Could this possibly be when Jesus "saw Satan fall like lightning from heaven?" (Luke 10:18) Who knows.
Not sure I'm making any sense here.

Maybe someone else is better able to take over
Ahh, this is why we talk and why forums such as this exist. To move closer to "any sense." It's a good discussion!