If God gave us free will.Why will he punish us for using said "Free will"If we are punished for exercising our free will, do we then have free will?

Free is not a biblical doctrine. No where in the word of God does it states anywhere that the Lord gave any of His creatures "free will". To have totally free will one, by mere definition, must be sovereign. God alone is sovereign! Here's several scriptures declaring this truth.

10 Therefore David blessed the LORD before all the assembly; and David said: "Blessed are You, LORD God of Israel, our Father, forever and ever.11 Yours, O LORD, is the greatness, the power and the glory, the victory and the majesty; for all that is in heaven and in earth is Yours; Yours is the kingdom, O LORD, and You are exalted as head over all. 12 Both riches and honor come from You, and You reign over all. In Your hand is power and might; In Your hand it is to make great and to give strength to all. 1 Chronicles 29:10-12

14 that you keep this commandment without spot, blameless until our Lord Jesus Christ's appearing, 15 which He will manifest in His own time, He who is the blessed and only POTENTATE, the King of kings and Lord of lords, 16 who alone has immortality, dwelling in unapproachable light, whom no man has seen or can see, to whom be honor and everlasting power. Amen. 1 Timothy 6:14-16

6 and said: "O LORD God of our fathers, are You not God in heaven, and do You not rule over all the kingdoms of the nations, and in Your hand is there not power and might, so that no one is able to withstand You? 2 Chronicles 20:6

10 He does great things past finding out, Yes, wonders without number. 11 If He goes by me, I do not see Him; If He moves past, I do not perceive Him; 12 If He takes away, who can hinder Him? Who can say to Him, 'What are You doing?' Job 9:10-12

13 "But He is unique, and who can make Him change? And whatever His soul desires, that He does. Job 23:13

3 But our God is in heaven; He does whatever He pleases. Psalms 115:3

5 For I know that the LORD is great, and our Lord is above all gods. 6 Whatever the LORD pleases He does, in heaven and in earth, in the seas and in all deep places. Psalms 135:5-6

10 The LORD brings the counsel of the nations to nothing; He makes the plans of the peoples of no effect. 11 The counsel of the LORD stands forever, the plans of His heart to all generations. Psalms 33:10-11

21 There are many plans in a man's heart, nevertheless the LORD's counsel—that will stand. Proverbs 19:21

24 The LORD of hosts has sworn, saying, "Surely, as I have thought, so it shall come to pass, and as I have purposed, so it shall stand:…27 For the LORD of hosts has purposed, and who will annul it? His hand is stretched out, and who will turn it back?" Isaiah 14:24, 27

12 Who has measured the waters in the hollow of His hand, measured heaven with a span and calculated the dust of the earth in a measure? Weighed the mountains in scales and the hills in a balance? 13 Who has directed the Spirit of the LORD, or as His counselor has taught Him?14 With whom did He take counsel, and who instructed Him, and taught Him in the path of justice? Who taught Him knowledge, and showed Him the way of understanding? 15 Behold, the nations are as a drop in a bucket, and are counted as the small dust on the scales; look, He lifts up the isles as a very little thing. 16 And Lebanon is not sufficient to burn, nor its beasts sufficient for a burnt offering. 17 All nations before Him are as nothing, and they are counted by Him less than nothing and worthless. 8 To whom then will you liken God? Or what likeness will you compare to Him? Isaiah 40:12-18

21 Do you not know? Have you not heard? Has it not been told you from the beginning? Have you not understood since the earth was founded? 22 He sits enthroned above the circle of the earth, and its people are like grasshoppers. He stretches out the heavens like a canopy, and spreads them out like a tent to live in. 23 He brings princes to naught and reduces the rulers of this world to nothing. Isaiah 40:21-23

10 Declaring the end from the beginning, and from ancient times things that are not yet done, saying, My counsel shall stand, and I will do all My pleasure,' Isaiah 46:10

9 All the nations gather together and the peoples assemble. Which of their gods foretold this and proclaimed to us the former things? Let them bring in their witnesses to prove they were right, so that others may hear and say, “It is true.” 10 “You are my witnesses, ” declares the LORD, “and my servant whom I have chosen, so that you may know and believe me and understand that I am he. Before me no god was formed, nor will there be one after me. 11 I, even I, am the LORD, and apart from me there is no savior. 12 I have revealed and saved and proclaimed— I, and not some foreign god among you. You are my witnesses, ” declares the LORD, “that I am God. 13 Yes, and from ancient days I am he. No one can deliver out of my hand. When I act, who can reverse it?” Isaiah 43:9-13

34 At the end of that time, I, Nebuchadnezzar, raised my eyes toward heaven, and my sanity was restored. Then I praised the Most High; I honored and glorified him who lives forever. His dominion is an eternal dominion; his kingdom endures from generation to generation. 35 All the peoples of the earth are regarded as nothing. He does as he pleases with the powers of heaven and the peoples of the earth. No one can hold back his hand or say to him: “What have you done?” Daniel 4:34-35

And just in case anyone have this crazy idea that God is not in total control over the devil, demons, evil, and wicked mankind, the scriptures declare:

4 The LORD has made all for Himself, Yes, even the wicked for the day of doom. Proverbs 16:4

 30 For the wicked are reserved for the day of doom; They shall be brought out on the day of wrath. Job 21:30

6 If a trumpet is blown in a city, will not the people be afraid? If there is calamity in a city, will not the LORD have done it? Amos 3:6

12 "If I were hungry, I would not tell you; for the world is Mine, and all its fullness. Psalms 50:12

So, what is it that the Lord God have given to the angels and mankind? The angels and mankind have freedom to do what God's governing laws of their respective realms allow, that is all. The angels are not free to become women and live amongst men. Mankind is not allowed to enter the spirit realm where God, the angels - holy and unholy, reside.

Angels and mankind are free to choose within the governing laws of their respective realms but they are not free to choose the consequences of breaking those laws. For example, God has instituted a little thing called gravity. You are free to exercise your will to go up to the top of a 30 story building. You are then free to choose to jump off the 30 story building however you are not free to choose the consequences of that choice. The laws of the Sovereign God now overrules your free will. It works the same way for the angels.

God, the Sovereign King and Creator have given His creatures freedom to exercise their will but only under the governing laws which He has established. Where His creatures rule, the LORD GOD overrule.

No one is punished for exercising free will. Everyone that is punished, is punished because they are sinners who willfully and continually violate God's sovereign laws.

Hope that helps.