Sorry for the delay, Cofty. Out of town and on my phone. I hope the formatting turns out okay.
I don't need the references. I've read all of the Old Testament.
Yes, God can do as he pleases. That's just what it means to be sovereign. Fortunately for us, He withholds the full weight of his power: He has not dealt with us according to our sins, nor punished us according to our iniquities (Psalm 103:10).
Now as for God condoning these things in giving the law, the law was never perfect or complete. It was a tutor (Galatians 3:24) that was supposed to make the Israelites realize their need for a Savior because without God, it was impossible to comply with the letter and spirit. You could make all of the sacrifices you wanted and be just as messed up and disinterested in God. So it wasn't following all the rules that ever made anybody righteous, it was always reverence for God and belief in God for his provision, his mercy and his own righteousness, which is Jesus (Romans 10:3). Jesus ultimately was the fulfillment of the law (Matthew 5:17; Romans 10:4).
So the law wasn't perfect as much as how to live best in a fallen world. At that time in antiquity, there were a lot of things historically that we don't experience today. To follow the letter irrespective of cultural context really misses the point.
One point I've thought of is that the law didn't always exist. The Ten Commandments (and more) obviously didn't come until Moses so people before Moses weren't under the law. (I pointed this out once when a JW tried to say that Adam was a murderer by some law of Moses. Adam didn't have the law).
My point was just that the law was given to help the Israelites avoid some of the mistakes that their forefathers had made. An example: don't take your wife's sister as a rival (Leviticus 18:18). That's obviously the case of Jacob. There was intense jealousy between Leah and Rachel then that hatred flowed down the line with Joseph being sold by his brothers into slavery. Which is never what was intended. The family is always supposed to be the strongest link as human relationships are concerned; that's the only "organization" God ever gave.
As for some of the things you mentioned--
Forced marriage/rape: this was unfortunately a protection to women, who were the most vulnerable in society. A woman who had been raped was essentially disqualified from marriage, which meant no one would take care of them or keep them in their household. So you see the example with Tamar after she was raped, she went into Absalom's household and he supported her (2 Samuel 13:20). Why? Because she was never going to be married after being violated by someone else. She even says to her rapist half-brother Amnon, not marrying me would be worse than what you have already done to me (2 Samuel 13:16). Because he wouldn't be taking care of her and would have had already subjected her to shame.
Yes, I'm glad to live in 2016 where I can support myself, live by myself and report a rape to the proper authorities. But again this is the cultural context that I was referring to--these things didn't exist. That's not how it was so it was the best solution.
Infanticide/genocide: this was a warrior/avenger culture and to leave even one behind was a liability. We see that sometimes where Doeg the Edomite comes and tells on David and gets all those priests killed or one person from the household remains and comes back and revenge is the house. So if one child remained in the family line, he would come back and avenge them. Also as a matter of worship, other cultures with showy overtures to their gods led Israel astray into the demeaning pagan rituals. We see that repeatedly throughout the Old Testament when they were around other nations, Israel did what they did, adopting those gods.
No intermarriage: because it would be a snare and lead the people to go after other gods and serve them. Solomon is the best example with his thousand wives that turned his heart from God. Also the Israelites returning to foreign wives in Ezra after the Babylonian captivity. Even though it wasn't a perfect solution, what do they do? They divorced their wives and put them out so that they wouldn't fall back into this system of idol worship (Ezra 10).
So all of these rules are meant to keep Israel under the protection of God, the only true God, the Lord. That's how I see it. In terms of God being a God of justice and righteousness, that is still there. The Old Testament is full of so many accounts where the Israelites go astray and then cry out to the Lord and he saves them. That's a repeated occurrence. The forgiveness of God is the exact exhibition of his mercy.
There is also His provision under the law for the poor-- not gleaning the corners of the field (Leviticus 19:9-10, 23:22) and the year of Jubilee when debts were released and land restored (Leviticus 25).
As I see it, the New Testament just adds a new "angle" to the Law and the Prophets. It doesn't really change anything, it fulfills it.
Jesus got angry, most notably throwing the money-changers out of the temple but pretty much any time the Pharisees tried to burden the people with their own rules or displayed their hypocrisy. Jesus's message was one of repentance that is turning back from sin and back to the Lord. The law which had become an instrument of oppression was given back its original intent of mercy and justice. The greatest commandment is the same as what we find in the Old Testament because Jesus quotes Deuteronomy 6:5: Love the Lord your God with all your heart, soul, strength and mind. Then love your neighbor as yourself (or do unto others as you would have them do unto you) is the second half of the Ten Commandments (also Leviticus 19:18). That's what those things are about. If anything, the New Testament just expands the concept of neighbor, not just fellow Israelites but all mankind.
The belief in life after this one (resurrection) is key to the Christian faith if you're looking from a justice perspective. Because obviously there are many instances of injustice in this world. Cases of poverty or illness or anything that might happen isn't necessarily a "judgment". It's just how Solomon says, time and chance happen to us all. But that itself is not always judgment on the person. The judgment on the person is always going to be based on what they did in their own lives, the decisions that they made. If you look at Revelation 20:12-13, when they're raised again, the dead will be judged according to their works whether good or evil.
But as I said, this isn't pie in the sky, do nothing faith. If you can do something to help right now, you should. Don't withhold good from someone who deserves it when it is in your power to do it (proverbs 3:27).
The law was always meant to look at how you're treating your neighbor. And I think that's what God is concerned about: how we treat other people and love for Him (which is made manifest in how we treat people, i.e., love one another).
I haven't had a chance to scroll through the latest pages but hoping that answers the questions so far.