Deuteronomy 5:31
But as for you, stand here by Me, and I will speak to you all the commandments, the statutes, and the judgments which you shall teach them, that they may observe them in the land which I am giving them to possess.
Deuteronomy 8:11
Beware that you do not forget the LORD your God by not keeping His commandments, His judgments, and His statutes which I command you today
Deuteronomy 11:1
Therefore you shall love the LORD your God, and keep His charge, His statutes, His judgments, and His commandments always.
Deuteronomy 26:17
Today you have proclaimed the LORD to be your God, and that you will walk in His ways and keep His statutes, His commandments, and His judgments, and that you will obey His voice.
Deuteronomy 30:16
in that I command you today to love the LORD your God, to walk in His ways, and to keep His commandments, His statutes, and His judgments, that you may live and multiply; and the LORD your God will bless you in the land which you go to possess.
This is abundant evidence to support the claim that the Law given to Moses was tripartite in nature: commandments, judgments, statutes. I will mention here, but not elaborate because the question doesn't provide an opportunity, that it mirrors the tripartite nature of both God, and man.
In Genesis 26:4-5 God says to Isaac:
And I will make your descendants multiply as the stars of heaven; I will give to your descendants all these lands; and in your seed all the nations of the earth shall be blessed; because Abraham obeyed My voice and kept My charge, My commandments, My statutes, and My laws.
It's the same tripartite division of the Law. So, in whatever modified form Abraham received instruction from God about his conduct among the nations, it would have been consistent with the Law as it was given to Moses. I can also mention, here, because it might spark a question for future investigation, Hammurabi reigned around 1770 BC, which puts him post-Abraham. This is cause to suspect the Code that is attributed to him had its source in the same tripartite Law that was given to Abraham.
Now, compare Genesis 26:5 and Deuteronomy 11:1, where Abraham and Israel are not only given the Law (commandments, judgements and statutes), but also a charge.
Abraham's charge - Genesis 12:1
Now the LORD had said to Abram: "Get out of your country, from your family and from your father's house, to a land that I will show you.
Israel's charge - Deuteronomy 1:8
See, I have set the land before you; go in and possess the land which the LORD swore to your fathers—to Abraham, Isaac, and Jacob—to give to them and their descendants after them.
The Law is the mechanism by which the charge is achieved. The process of application of the law and reaping the fruit thereof, advertises the goodness of God to the nations of the land, i.e. glorifies Him.
Who else received a charge and the tripartite Law?
Adam and Eve's charge - Genesis 1:28
Then God blessed them, and God said to them, "Be fruitful and multiply; fill the earth and subdue it; have dominion over the fish of the sea, over the birds of the air, and over every living thing that moves on the earth."
Based on a Genesis 4:7, I can safely contend that Adam and Eve received the law, because their son was familiar with it. God addresses Cain in this way:
If thou doest well, shalt thou not be accepted? and if thou doest not well, sin lieth at the door. And unto thee shall be his desire, and thou shalt rule over him.
This is the first time sin is mentioned in the Bible, and God uses this encounter to establish the framework in which sin arises - the Law (doing and not doing well), natural inclinations (desire), and the need for restraining those inclinations (ruling over them). God doesn't elaborate on what "doing well" meant for Cain, apart from a requirement related to "offerings", but we can be pretty certain that Cain knew all about the rules, and that they would have been consistent with what we have received through Moses.
Conclusion
There is good reason, here, to support the claim that all the sons of God - those who call upon the name of the LORD - are introduced to the same commandments, judgements and statutes as Abraham and Israel. So, whether Job was pre- or post- Abraham, he knew what "doing well" and "not doing well" meant in regard to his relationship with God.
Addendum
You ask:
Additionally, the heading to chapter 9 says Job Says There Is No Arbitrator between God and Man, yet I cannot find anything in the passage that clearly supports this. As I noted above, we clearly see God referencing how he felt about Job, but how did Job feel about how he could speak to God?
I think the absence of detail about Job -> God communication is a significant sub-issue of the story.
Job was a diligent practitioner of his religion and the blessings that came to him are obvious and many, but one gets the distinct feeling that his relationship is somewhat ritualistic. Job 1:5 records:
So it was, when the days of feasting had run their course, that Job would send and sanctify them, and he would rise early in the morning and offer burnt offerings according to the number of them all. For Job said, "It may be that my sons have sinned and cursed God in their hearts." Thus Job did regularly.
Job is motivated by a genuine concern for his family and the knowledge that his adherence to the law is a winning formula. It should be noted, here, that "sanctification via burnt offerings" is a distinct link to the tripartite Law I mentioned above.
Job 42:5-6 gives us Job's declaration of repentance:
I have heard of You by the hearing of the ear, But now my eye sees You. Therefore I abhor myself, And repent in dust and ashes.
Job's connection to God prior to his misery was impersonal - a diligent application of the rules that came to him by "the hearing of the ear". Job -> God communion only became more than this when he was compelled to petition God about a reason for his misery.
Chapter 29 of the story gives a strong indication that Job's advertising of the goodness of God was minimal at most. It seems His own goodness was uppermost in his mind:
Job 29:7-11
When I went out to the gate by the city, when I took my seat in the open square, the young men saw me and hid, and the aged arose and stood; The princes refrained from talking, and put their hand on their mouth; The voice of nobles was hushed, and their tongue stuck to the roof of their mouth. When the ear heard, then it blessed me, and when the eye saw, then it approved me;
Job 29:21-25
Men listened to me and waited, and kept silence for my counsel. After my words they did not speak again, and my speech settled on them as dew. They waited for me as for the rain, and they opened their mouth wide as for the spring rain. If I mocked at them, they did not believe it, and the light of my countenance they did not cast down. I chose the way for them, and sat as chief; So I dwelt as a king in the army, as one who comforts mourners."
Job 29:12-17
Because I delivered the poor who cried out, the fatherless and the one who had no helper. The blessing of a perishing man came upon me, and I caused the widow's heart to sing for joy. I put on righteousness, and it clothed me; My justice was like a robe and a turban. I was eyes to the blind, and I was feet to the lame. I was a father to the poor, and I searched out the case that I did not know. I broke the fangs of the wicked, and plucked the victim from his teeth.
Contrast Job's words with those of Moses. Deuteronomy 32:1-4 records:
Give ear, O heavens, and I will speak; and hear, O earth, the words of my mouth. Let my teaching drop as the rain, my speech distill as the dew, as raindrops on the tender herb, and as showers on the grass. For I proclaim the name of the Lord: Ascribe greatness to our God. He is the Rock, His work is perfect; For all His ways are justice, a God of truth and without injustice; Righteous and upright is He.
Where in Job's words is there evidence of the same desire to advertise the goodness of God? Job's words are self-approving rather than God-approving.
There is much more that can be said about this fascinating story and its identification of the source of human suffering, but that's for another time.