Chapter 16 starts off with Sarai and Abram(since he did agree to it) trying to fulfill God's promise on their own in their timing not God's. Basically like so many of us they got impatient and didn't have complete faith in God. For me personally I think that maybe the is one of the most difficult things is waiting on God's timing, even thought I know His plans always workout much better than my own.
Hagar, Sarai's servant shouldn't have looked down on Sarai just because she got pregnant. She took an already touchy situation and made it worse. She should have b been grateful for the privilege to have the opportunity to have a child.
Drama from taking on a second wife here and they complications from it , is why God wanted marriage between one man and one woman (Genesis 2:24) There are other instances in the old testament that a man has more than one wife and almost always there are issues because of it.
God being a merciful God takes the mess they made and make the best of of it. Verse 16:13, "...'You are a God of seeing,' for she said, 'Truly see I have seen him who looks after me.'" Just like with Hagar God is watching over you! He see what's going on and has plans to make it better. Remember Jeremiah 29:11 " For I know the plans I have for you, declares the Lord, plans for welfare and not for evil, to give you a future and a hope."
Chapter 17 at ninety nine years old God changes Abram's name to Abraham to confirm the promos He gave him years prior that he would be the father of a multitude of nations. As the sign of this covenant every male had to be circumcised in other to be part of the blessings. It wasn't just Abraham's blood family but everyone in the household.
Some could take the next part of Abraham and Sarah having a child past the time of the natural bing able to have kids as God showing off. But when God does things like this it is more about making people truly understand how powerful God is and how much we really need Him.
I feel like there maybe some significance that God tells Abraham and Sarah that Issac will be born in one year, right before He has Sodom and Gomorrah destroyed.
Abraham I am sure is trying to save Lot but he also wanted to save everyone because if it was just about Lot he could have just asked God to spare Lot's family. God was will to spare the city even if they only found 10 righteous. God really doesn't want anyone to perish which is why He gives warning and is what we perceive at times as being slow to act, but 2 Peter 3:9 shows the reality that God is just being patient with us.