How about some scripture addresses?
Check Genesis 12
(and surrounding if you want more context
) for the start of the covenant. Gen12 is where God introduces the "seed"/"offspring" promise, which Paul explains in Galatians 3
For the covenant made with Moses (Mosaic Covenant), jump to Deuteronomy 28
. There they lay out the terms for blessings and curses (penalties). The curses are the inverse of the blessings, with more detail. When making the covenant with Israel (Mosaic Law), that included the laws you mentioned. Adding to Nate, the Mosaic contains moral, civil, and ceremonial laws.
Covenants are just contracts. They can be unilateral for fulfillment, or bilateral. They have the parties involved, time, scope, consideration, duties, requirements, and penalties, etc. It's just like any business contract.
The 10 commandments are primarily outside the Mosaic Covenant, despite their close proximity, but then are also included in it. That may make it a little confusing. They are the moral law that NateR mentioned. Thus, they are still in effect. They also aren't random, but reflect God's character (see R C Spraul). The moral law, reflecting God's character, is why Jesus & Paul refer to creation regarding certain topics. The Mosaic Covenant's time ended with Christ, the "seed," as explained in Galatians 3.
So, does the close of the Mosaic Covenant make all that history useless? No. As Israel floundered between faithfulness and rebellion ("adultery" against God), we see that God kept up His end of the agreement. That's the whole context of the remaining OT. So, as the prophets give warning, they are warning that God will uphold his end of the bargain. Much of the Mosaic law tells us about God's character, his purity, sinless-ness, and faithfulness toward us. So, we can look at it as a guide to who God is. Check out the comments in Exodus 34
Then we can understand the covenant of Grace. Re-read Chris's post about 1 John.
The previous answers were really good. I hope some chapter numbers & reading will help see it put together. Thanks for reading.