Abram Turns to Abraham

Covenant. A word I can't seem to understand in the bible. What exactly is it talking about? Because I can't seem to find the answer to that question. All that comes to my mind, when I hear the word "covenant", is Ireland. (I won't even begin to expain that.) So what exactly is the covenant God is talking about to the now-known-as Abraham dude?
So what I understand of the chapters, is that the LORD went to visit Abraham's cozy tent. Unless of course, God goes there in spirit. [ooooh] But now I'm confused. It says, "Because the cry of Sodom and Gomorrah is great, and because their sin is very grievous..." (Genesis 18:20). What exactly did they do? I don't think I'm getting much sleep because I have no idea what the Bible is talking about at this point. Maybe it has something to do with the fact that I'm skimming through the chapters and verses and blah, blah, blah. But what did Sodom and Gomorrah, whoever they are, do that made them so very sinfull and made God pay a visit?
Okay, now I feel stupid because I just read a little more and realized that Sodom and Gomorrah, are indeed two cities. Yes, they are cities, not human beings. So now I know that God was paying the two cities a visit because they are unbelievably wicked. In other words, he wants to destroy them.
No offence but what is with God destroying things? Has anyone else realized that he always seems to destroy people and places whenever people are becoming too wicked or doing something they're not supposed to? All I know is that I'm surprised our planet hasn't been destroyed, cause there's some seriously wicked people out there.
So anways, back to the Bible.
God makes a deal with Abraham that he won't cause chaos in the two cities if there are fifty righteous people. Then the two fought some more and it was decided that if ten righteous people were found then the city won't be destroyed.
This guy Lot then offers his two daughters unto, someone, while he says that the, someone, cannot touch these two guys because they're under the protection of his roof. (Yet another example of how back then women were nobody's and men were everything.) And then God decides to save this dude Lot from the destruction of the city and sends them away to Zoar.
What the heck is going on?
As it turned out, the two cities were destroyed.
As the story goes on, Abraham and his wife were promised the son they had wished for. His name was Isaac. Then one day, the LORD told Abraham to sacrifice his son. Abraham did this sadly, but without doubt or hesitation. He trusted God. Abraham took his son to a place to do the sacrife where Isaac asked, "Behold the fire and wood, but where is the lamb for a burnt offering?" (Genesis 22:7) Abraham told his son there was no lamb, just Isaac. As Abraham was about to do the sacrifice, God stopped him and told him Isaac no longer had to be sacrificed. Because Abraham was willing to do anything for God, he was blessed greatly.
In the end, Abraham's wife died and he decided to find Isaac a wife.
Rebekah was found and Isaac and her were wed.