At 2 Cor 4:4. Do you believe Paul when he wrote 'Satan is the god of this world'? So is Satan a god? ?

well ............it says so, so yes he is a god, a false god

1 Corinthians 8:5 For even though there are so-called gods, whether in heaven or on earth, just as there are many “gods” and many “lords,” 6 there is actually to us one God, the Father, from whom all things are and we for him; and there is one Lord, Jesus Christ, through whom all things are and we through him.

Zeus is the god of the ancient Greeks.  Does that mean Zeus is a god?  

Well, if you mean, do people worship him, okay, some people worship Xi Jinping.  They don't call him a god, but they treat him like one, and actions speak louder than words.  I see more people worshiping Satan - that is acting as though he were their deity - than worshiping God.  

The Bible is full of mention of false gods. Some are named, especially amongst the polytheistic, pagan religions. But the Bible is consistent in saying there is only one TRUE God - all the others are false. Yet it also says that demons are at back of these false gods: "The sacrifices of pagans are offered to demons, not to God" (1 Cor 10:20). And the chief of the demons is Satan who rules over them and those who unwittingly worship them, as "the god of this age who has blinded the minds of unbelievers so that they cannot see the light of the gospel of the glory of Christ, who is the image of God. For we do not preach ourselves but Jesus Christ as Lord" (2 Cor 4:4-5).

Satan is the invisible ruler who gets power through deception. He is described as "the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient" (Eph. 2:2). Christians used to be controlled by that evil, invisible spirit power until the gospel of salvation in Christ translated them into the Kingdom of God. So, there is only one TRUE God - the Creator - and there's only one Creator. All others claiming the title 'god' are would-be-usurpers, false gods.

As for Psalm 82:6 and John 10:34, Jesus was in danger of being stoned to death for alleged blasphemy when He said His Father was God, so He pointed out to those religious zealots that even men appointed to represent God on Earth in positions of judgment were called 'gods' due to their right to receive respect from other men; His antagonists ought to have shown Him respect even if they didn't believe His Father really was God.

No.  Paul was using hyperbole to make a point.  Most people certainly follow him to a greater or lesser extent.

The verse states "god of this world". The "g" is in the lowercase, which means Satan is a false god. Any god with the "g" in the lowercase is a false god.

Only the true God is capitalized in the Bible.

2 Corinthians 4:4 “In whom the god of this world hath blinded the minds of them which believe not, lest the light of the glorious gospel of Christ, who is the image of God, should shine unto them.”

Of course Satan isn't a god. He is the ultimate loser of all time. However humans can make various things their "god", that is, the principle guiding force in their life - money, fame, sex, their job, etc. And Satan does his best to get us to do so.

small g should tell u something...SAtan likes to elevate himself but he will end up in fire with his followers..Sinning in HEAVEN IS TOO STUPID to believe..

The Word declares the advisory is the ruler of this world. It was conferred unto him when Adam sinned as the gospel of Luke states.

Basic principle: You cannot give something away that you do not possess.

Luke 4:5-7

4:5And the devil, taking him up into an high mountain, shewed unto him all the kingdoms of the world in a moment of time.

4:6 And the devil said unto him, All this power will I give thee, and the glory of them: for that is delivered unto me; and to whomsoever I will I give it.

4:7 If thou therefore wilt worship me, all shall be thine.

II Corinthians 4:4

The god of this age has blinded the minds of unbelievers, so that they cannot see the light of the gospel that displays the glory of Christ, who is the image of God.

Where does that say anything about Satan?

I believe Paul was a tad off his rocker or an excellent conman.