The OP states that Calvinism--apparently referring to the TULIP doctrine--is the Gospel, and that it will defend Calvinism by showing that Calvinism is the Gospel, which is necessary because its detractors criticize it as a perversion of the Gospel. However, the defense is not presented, so the criticism remains: Tulip perverts the Gospel by denying, ignoring or contradicting Scriptures teaching that God loves the world, wants everyone to be saved, and does not show favoritism, such as John 3:16, 1Tim. 2:3-4 and Rom. 2:11.
As to John 3:16 - it would help you a lot, if you would remember, that this verse is just one of many in this ongoing conversation with Nicodemus. The entire conversation goes from verse 3 to verse 21. You can't cherry pick verse 16 and ignore the rest. Our Lord explains to Nicodemus, (Who should have known these things), that one has to be born from above in order to perceive and enter the the Kingdom of God. (Verses 3-10) He confirms, that whosoever is believing in Him, has been born from above. (Verse 8) He tells Nicodemus: "I told you terrestrial things and you did not believe, how could you possibly believe if I told you heavenly things?" (verses 11-13: The need for the new birth being emphasized.). Verses 14 and 15, will fulfill the foreshadowed event from the OT.
Verses 16 and 17 must be seen as one complete thought. God expressed His love for the world by sending His Son to redeem those the Father gave to the Son, from all eternity. (John 6:37; 10:29) This purchased for all of humanity time because as verse 17 states, He did not send the Son, this time, to condemn the world, rather, He sent Him to finish the work of salvation.
Verses 18-20, explains how fallen man hates the light because mans deeds are evil continuously and will not come to the light because if he did, they would be exposed. Verse 21 - is the good news. For all that do come to the light, they are wrought of God. What is this old English word wrought? It means: fashioned, created or work. John 3:21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought (created - fashioned) by God. So we started with what God does in the new birth and finished here, with the deeds of believers which are the creation of God as well. Php_2:13 For it is God which worketh in you both to will and to do of his good pleasure.
1 Tim. 2:3 & 4 - You are referring to the word "all" in this verse. The "all" in the English language can have two specific meanings but can be used about seven different ways. The two specific meanings have one similarity and that is, that they both mean "totality". It therefore, can mean total in number or group. It can also mean, total in type or manner. In the case of it's usage in 1 Timothy 2:4, it means "all types" or "all manner of" men. This is distinguished by the context of verses 1 and 2. The writer is discussing prayer for Kings and men in authority - all manner of men. What are we praying for? Verse 2b - ..that we may lead a quiet and peaceable life in all godliness and honesty. Verse 3 - then tells us this is what's - good and acceptable in the sight of God our Saviour;