Was the covenant with Adam suspended or replaced by the covenant with Noah?

I see that you are an inquisitive Christian, that's excellent, never stop reading the Bible and asking God to show you the truth.

The covenants is a complex topic that requires deep study, and depending on the Christian denomination you may get different interpretations.

God's covenant with Adam was the covenant of grace, salvation through Christ. It is the same covenant as the ones He renewed with Noah and Abraham.

There is another covenant that was introduced to the Isrealites after Egypt that we call the 'old covenant', but its purpose was to use the law to show them their dependance on the original covenant of grace, and show the impossibility of keeping the law by themselves. Thus when Jesus later told the Jews about a new covenant, he was referring to the original covenant of Grace.

I find the writings of a Christian writer Ellen White helpful:

As the Bible presents two laws, one changeless and eternal, the other provisional and temporary, so there are two covenants. The covenant of grace was first made with man in Eden, when after the Fall there was given a divine promise that the seed of the woman should bruise the serpent's head. To all men this covenant offered pardon and the assisting grace of God for future obedience through faith in Christ. It also promised them eternal life on condition of fidelity to God's law. Thus the patriarchs received the hope of salvation.

This same covenant was renewed to Abraham in the promise, "In thy seed shall all the nations of the earth be blessed." Genesis 22:18. This promise pointed to Christ. So Abraham understood it (see Galatians 3:8, 16), and he trusted in Christ for the forgiveness of sins. It was this faith that was accounted unto him for righteousness. The covenant with Abraham also maintained the authority of God's law. The Lord appeared unto Abraham, and said, "I am the Almighty God; walk before Me, and be thou perfect." Genesis 17:1. The testimony of God concerning His faithful servant was, "Abraham obeyed My voice, and kept My charge, My commandments, My statutes, and My laws." Genesis 26:5. And the Lord declared to him, "I will establish My covenant between Me and thee and thy seed after thee in their generations, for an everlasting covenant, to be a God unto thee and to thy seed after thee." Genesis 17:7.

Though this covenant was made with Adam and renewed to Abraham, it could not be ratified until the death of Christ. (Patriarch and Prophets, pg 370)

Have a read, it's several pages. The book also covers creation, the fall, and God's loving relationship with the early patriarchs really well (like Abraham, Issac, Jacob and Moses). I find it adheres to the Bible.

All the covenants are connected, not replaced or suspended. They work together and show us God's plan for Salvation. 2 Samuel 14:14 The promised "Seed" was the basis for salvation "under Adam". Then covenant with Noah was to remove the curse of the Earth, eventually or in the future in God's kingdom. The covenant "with Abraham" leads us to the promised "seed" which is The Christ, head and body. It also includes the Jewish people to bring the blessings to the Earth in God's Kingdom. Both Jews and Gentiles participate in the blessing of the world (Hebrews 11:40) Jesus is the only way into God's kingdom. When Adam and Eve were thrown out of Eden and the way back was guarded by flaming swords (Genesis 3:24), the only way back is through Jesus, the gate. All the covenants work toward salvation and they work together. They show God;s Grace and desire to reconcile with mankind after the law is written in their hearts.

The Adamic Covenant is found in Genesis 3:16-19. As a result of Adam’s disobedience sin entered into the world, and death through sin. Death is the inescapable fate of ALL of Adam and Eve’s descendants. In other words, it applies to all humanity. That covenant has not been revoked.

The Noahic Covenant, found in Genesis 9:8-17, is the promise that God made to Noah and his descendants after the flood which destroyed the world. It is an unconditional covenant and it was made to Noah and ALL his descendants as well as “every living creature” and the earth in general (Genesis 9:8-10). That covenant still applies, and the rainbow in the sky reminds us that God will never again destroy the world by water.

The Abrahamic Covenant is God’s promise to bless Abraham (Genesis 12:2), that Abraham would have numerous descendants (Genesis 13:16), and that he would be the father of a multitude of nations (Genesis 17:4-5). God also made promises regarding a nation called Israel. God promised that the families of the world will be blessed through the physical line of Abraham (Genesis 12:3; 22:18). This is a reference to the Messiah, who would come from the line of Abraham. The Palestinian, or Land Covenant (Deuteronomy 30:1-10) expands on God’s promises to Abraham.

God has made four covenants with the nation of Israel: Abrahamic, Palestinian, Mosaic, Davidic. Three of those covenants are unconditional, i.e., regardless of Israel’s obedience or disobedience, God will uphold his end of the covenant. Only the Mosaic covenant is conditional, i.e., this covenant will bring either blessing or cursing depending on Israel’s obedience or disobedience.

Because it is impossible for imperfect people to keep God’s perfect laws, the Law (as handed down to Moses and the nation of Israel) condemns. That is why God introduced a New Covenant. It’s in Jeremiah 31:31-34. All who enter into the New Covenant will be set free from the penalty of the Law, which condemns.

The Christian perspective is that Christ Jesus has fulfilled the Law of Moses (Matthew 5:17) and the New Covenant provides the opportunity to receive salvation as a free and undeserved gift (Ephesians 2:8-9). Christians believe the New Covenant is not restricted to Israel but is open to Gentiles (non-Jews) who come to saving faith in Christ Jesus.

Edit: The basis for salvation from Adam till Jesus is faith in God and in God’s promises. Hebrews chapter 11 lists many Old Testament characters who, because of their faith in God, were assured of being the recipients of God’s promises:

”All these people were still living by faith when they died. They did not receive the things promised; they only saw them and welcomed them from a distance. And they admitted that they were aliens and strangers on earth... Instead, they were longing for a better country – a heavenly one. Therefore God is not ashamed to be called their God, for he has prepared a city for them” (Hebrews 11:13-16).

The Adamic Covenant is still in force as evidenced by the fact we still die. It also points forward to the time when the last enemy, death, will be destroyed. Jesus’ resurrection showed how death could be defeated and after the millennial reign of Christ, sin (and its consequences) will be no more.

The Noahic Covenant (that God will not destroy the world by flood) is still in force as evidenced by the rainbow in the sky. It has nothing to do with our eternal salvation or with the Abrahamic Covenant and applies universally to peoples.

The Abrahamic Covenant embraces the promises made by God to Israel. The promised blessings to Abraham’s descendants have been partially fulfilled in the coming of the Messiah (who came through the line of Abraham). The full restoration of Israel awaits the second coming of Christ.

Three of the seven covenants (Adamic, Noahic, New) are made between God and mankind in general, and are not limited to the nation of Israel. All of the Covenants God has established are integral to the ultimate fulfilment of God’s purposes which culminate after the millennial reign of Christ and the final conflict when He destroys Satan and all who follow him. So, the answer to your question is no, in the sense that all those covenants are still in force, although they all point to the New Covenant. And the basis for salvation always has been and always will be faith in God and in his promises to bless all who turn to Him.