What promise did God make to Abram in the context of cutting a covenant and explain the significance of this ritual?

Answer 1

God made two covenants with Abraham (Genesis ch.15 and Genesis ch.17), and one with Abraham's Israelite descendants in the time of Moses after the Exodus.
1) In Genesis ch.15, the Covenant Between the Parts:
a) God informs Abraham of future events (the Egyptian exile)
b) God promises the land of Canaan (Israel) to Abraham's descendants
c) The covenant is finalized through a demonstration of God's presence (see Genesis 15:7-9 and 15:17).

2) In Genesis ch.17, the covenant of circumcision:
a) The promises of many descendants (17:2,3) and of inheriting the land of Canaan are repeated (17:8), but the main thing in this covenant is the promise that God will be the God of Abraham (17:7, 17:8).
b) God promises that Abraham and Sarah will have a son (17:15-16), whom they will name Isaac (17:19) and who will be the continuation of God's covenant with Abraham (17:21).
c) The covenant itself is manifested through circumcision, for Abraham and his descendants (17:10).