So the basic justification of the medieval system, as I'm understanding it, was that these temporal authorities, this legal system, etc., was ordained by God. Additional ideas suggested are that the king was idealized as the representative of the people, and that medieval system was organized for the wellbeing of society. Both of those seem, thought, at least to me, to be something of presentism; were those ideas really around before the Renaissance?
Yes.
The "well being of society" was looked at in a way that post-Enlightenment anti-monarchists can't distinguish from barbarous despotism, but it was still used. Each man in his place was the best arrangement for society according to the philosophy of the time.
Various attempts to claim God's approval of what had been arranged for whatever reasons, based on it being somehow in adherence to God's will that things be thus.Additionally, how was the specific legal system of the medieval ages, descended from Roman law or made up on the spot, justified as ordained by God? Was the issue of its arbitrary nature just glossed over, or did they have some solution like (just to pick a random idea) "This legal system is created by Christians and the authority of the church, and so it is ordained by God," or others?
Of course, everyone is, I think, aware that this is all so much propaganda, and that everyone just did what they could get away with, and justifying their actions was part of this.
There are a multitude of theories on the issue, the Middle Ages was less concerned with settling on or debating why it was okay as saying that it was.