This part of the chapter almost seems parenthetical to me. It relates the failure of Isaac to protect the reputation of his wife, Rebekah, by perpetuating a lie that they were brother and sister much like his own father, Abraham, had done a couple of times to Sarah. But if the narrative of the marriage of Isaac and Rebekah is told sequentially it makes me wonder where the children were during their sojourn with Abimelech of Gerar in Philistia. Verse 8 states that they had been there a long time and I suspect that it would be difficult to keep up the charade with small children present.
Another possibility is that the boys were already grown and living elsewhere, like shepherds of their father's flocks, since the end of the chapter tells of Esau's marriages to women who were a constant aggravation to his mother.
Does God make any promises in this passage?
God appeared to Isaac at Beersheba and promised that He would be with him and would bless him just as He had blessed Abraham. He also stated that He would do this for Abraham's sake.
Are there any references to Jesus?
The analogy is often made of Jesus being the spring of living water (verse 19). Isaac's herdsmen fought with the herdsmen of Gerar over it and lost. They then moved and dug another well that they called Sitnah which means enmity. They lost that one also. Then they dug a third well which they were able to hold without a fight and they called it Rehoboth which means broad because God had made room for them. There is an analogy here of the first state of man (spring of living water) being lost during the first battle with the serpent, progressing to the life of constant battle with Satan, which will eventually be followed by life with the One that has made a place for us. There was also a fourth well called Sheba which means an oath, and the city named Beersheba which means well of the oath. Jesus is the Oath, or promise, that supplies peace between God and all people who repent and believe on Him.
Are there any references to End Time events or eternity?
As mentioned above, Jesus has prepared an eternal place for us. It is our Rehoboth and Beersheba.
Does God issue any commands in this passage?
He told Isaac not to be afraid because God would always be with him.