Q1) From Adam to Moses there was no law. Are they free from judgement?
A1) We see an example of Adam and Eve being held accountable for their sin of eating from the forbidden tree, which is log before God prescribed the Mosaic law.
We also see Cain judged for his sin, once when he made a sacrifice that was not pleasing to God, and again when he was punished for killing his brother Able. So while the Bible does not describe how Cain and his family were able to understand what was morally expected, we see evidence that they were indeed responsible for their actions due to knowing better but choosing to do otherwise.
Q2) From Moses to Jesus there was written law nobody could live up to?
A2) This is true, and by God’s design. But why? God set the moral standard by His standard instead of by our ability to meet it. And of course God’s standard is to expect perfection. The law was given so that we could see from experience that we fall so short of God’s glory (Romans 3:23). See also Romans 3:20 on more about the law being given to show us we can’t hold up to God’s standard.
And the prescription for repentance was that blood must be shed, to demonstrate how sever the situation of sin is
But, all the while those before Christ, just like those who have lived since, are all saved by the same means. We are saved by faith in the Messiah who came, and whose name we know to be Jesus. Those before Christ were saved by faith in a Messiah who was to come, whose exact name they did not know except as prophesied by Isiah like in Isaiah 9:6 or in Isaiah 7:14
Q3) Jesus gave us the holy spirit as our conscience or law written in our hearts. Did people have a conscience before the holy spirit?
A3) The conscience is a God given part of our body or spirit that the Holy Spirit directs and uses. The Holy Spirit is not our conscience, but does influence our conscience, like for example when we are convicted of sin, or being directed toward truth or away from lies. But our conscience can be corrupted just like the rest of our body or lifestyle if we train our conscience negatively.
So yes, people have always had a conscience, though there was a time where people did not have the direct access to God/Holy Spirit the way we do now. Which is why God, as you said, wrote the law on ur hearts from the beginning of time.
For example, one may decide that they are justified in stealing, but if they are stolen from, they feel wronged. Because no matter how you justify it, you know deep down that stealing is wrong, and you don’t need the Bible or the Holy Spirit to tell you this, because we are born with an inherent sense of right and wrong written on our hearts.