There are many different types and levels of covenants. I shall only look at a few of those most commonly seen in the Scriptures. The first type is called a royal grant. The royal grant is a covenant made by only one side of those involved and is typically unconditional. Examples of this include the promises YHVH made to Noah that He shall never again flood the world, the promise to the priest Phineas to have an everlasting priesthood, and the promise to David to have a descendent on the throne forever. There is nothing required of the second party in this type of agreement and therefore nothing that the second party does can change it.
The second type is a king/subject covenant where there is a greater and a lesser partner. For example, a king promises protection and care of an individual if the individual will help support the king with food or with manpower in a time of war. This type of covenant is often a conditional agreement. If either side breaks the requirements, then the other party is released. We see YHVH make this type of covenant with Abraham and again later with Israel at Mt. Sinai. The basis here being that if they will be His people (obey Him), then He will be their Mighty One.
The third type is a person to person or group to group covenant where all involved are equals. This type also tends to be conditional and can be broken by either party. In the Bible an example of this would be David and Jonathan with their promise to help and care for each other (something that proved difficult under Saul's dislike for David).
Covenants can be made many different ways, but the most common are the verbal or the ceremonial agreements which include what is expected of both partners. Nowhere do we see all of these customs used together in one ceremony, but the following are a few of the symbols used in the Scriptures.
The cutting of a covenant is one of the most well known. In this method, animals are cut into two pieces and the individuals making the covenant come together between the pieces and proclaim that if they do not keep this covenant, may they be cut up like these animals (keep in mind that oaths, blessings, and cursings all have their effect in both the physical and the spiritual ... this is no light thing to say). When YHVH makes this covenant with Abram, it is somewhat unique in that only Elohim went through the cut animal pieces ... in essence making it a one-sided covenant promise.
Another type is a blood covenant which includes one's direct descendants (bloodline). Because this type of covenant includes a persons descendants, it comes close to paternity (literally defined as under the girdle). This paternal aspect helps to explain why circumcision became a symbol of the covenant with Abraham and the nation that was to come from him. In these covenants, one is ready to give not just one's own life, but also that which is dearer than ones own life to help another. This was part of the testing of Isaac, to see if Abraham would genuinely love YHVH so much as to give up his son. Making a covenant genuinely means withholding nothing from the partner.
With Jonathan and David we see the exchanging of robes. They gave their love to each other as closer than family. They went a step further and exchanged weapons as well which shows their protection for each other. We have the same thing happen when we enter into covenant with Messiah. We are clothed in His righteousness. We receive His power for our protection. When the enemy attacks us, His weapons are at our disposal for He is on our side. Conversely, we are on His side and should be ready to uphold His name and act for Him as well.
We should realize that typically there is no room for mercy in a covenant. When one side messes up, there is a punishment waiting. However, the Father is Merciful. He makes provision for mercy through atonement. When someone would sin, it could be placed upon an animal and it would be torn up (sacrificed) instead. Yahshua's atonement on the cross was another great act of mercy ... the greatest act of mercy possible. Humans have broken the covenant many times, were it not for the mercy of Elohim, we would be long gone ... the covenant null and void. But through His love, it continues.
I am not sure how many different covenants are in the Bible, but there are many and we should not confuse them or blend them together. The covenant made at Mt. Sinai is not an extension of the Abrahamic covenant. Abraham was promised many descendants and land. The Nation of Israel was promised prosperity for their obedience. It is an amazing thing to read through the Scriptures and look at it from the covenant perspective. Everything YHVH does is based on the covenants He has made. All of His actions recorded in the Scriptures and the effects that have happened through history for Israel line up and match exactly what is stated in those covenants.
Many people seem to describe the Mighty One of the Old Testament as angry, mean, and wrathful because of all the trials and tribulations Israel went through. What I see is that Israel suffered the very things they agreed to if they would not follow the Almighty's commands. Israel's eventual captivity and dispersion was for their complete abandonment of Elohim altogether ... exactly what the covenant details described. Conversely, people view the New Testament as being full of mercy and favor. This is true for the believer. But we also find numerous rebukes and scathing remarks for those who rebel. In the end, we read of final judgment and destruction for those who do not keep His covenant.
Elohim, acts like a father (He is our Heavenly Father). He disciplines and corrects His children as any parent would do. We are not referred to as His children for nothing. As His sons, we are the builders of His name and of the reputation of His house. We need to uphold the Honor of the One whom we are in covenant with and act as He would act. Otherwise, we tarnish His reputation ... which is not acting like a person who is in covenant.