Actually this is really a weird situation. When Roman law was in it's developing stages, there was a lot of wrangling about what to do. The law evolved in 2 very important steps.
1. This is very important. About the 5th century BC, it was thought best to write the laws down. That way a magistrate would be bound by what the law said, as would every other magistrate. The starting point would be the same for everyone. That meant that if someone deviated from what was written, there was a written reference. Everyone had the same written reference. And appeals could be based on the written Roman Law. So codification of the law belongs to both Rome and Greece, but mostly Rome.
Rome did contribute one thing (but they got part of that from the Greeks). When they got around to codifying the law, the made it into a science of sorts. The Greeks didn't do that. But the idea of what the scientific method was, came from Greece.
So far what you see is Rome "borrowing" an idea from Greece and adding to it.
2. Guess where they stole the model for the 12 tables from? (this is the Roman version of the law). That's right, another thing stolen from Greece. Not just Athens. There were many cities that received Romans seeking models of the law. This last comment is disputed a bit by modern historians. They do not believe that Rome would send her noble class all over conquered Greece to get information. The historians of the time, thought that was the way it happened. I'll go with the people who were actually there. Roman historians for me.
In Government, I think your first and most promising answer is democracy developed in Athens. Who could speak and under what circumstances, and when debate was ended are all complex issues. The Romans preferred a Republican model. Let the upper classes do the ruling, but if you were a member of the senate, you could speak openly and have any opinion and defend it until debate ended. I'm not sure how the end of a debate was decided. I have the impression that one of the strongest points the Romans had was their tolerance. You could believe anything you wanted as long as it did not interfere with government. Even Jesus recognized this as a virtue. Do you remember what he said about the Roman Coin when asked? He said ‶Give unto Rome what is Rome's, and give unto God what is His.″ That's really amazing when you think about it.
Greece had the same open door policy, I think, or at least Athens did. Athens tolerated all sorts of governments to flourish, religions as well . As far as I know (check this) she never went to war with either Sparta or Thebes and if she did, it wasn't over their form of government, which was quite different.
Two
I have read all sorts of reasons for the fall of the Roman Empire. Realize that you are talking about an institution that stayed in power for about 1000 years. Who has matched that?
Everything is possible. Everything. One scholar believes it was lead in the pipes transporting the water was the cause. Another believes that the Goths (and their ‶cousins″ could not be defended against. Another thought it was because the army was paid in debased currency. Still another thought it might be the debasement of their currency. I like the possibility that the empire was split in 2 by Constatine which allowed the Eastern Empire to remain for many many years. Still others thought it was corruption that ended the integrety of the of the ruling classes. I don't know what you are going to pick.
There are all sorts of reasons offered from psychological to physical to military, and it really does depend on what period you begin with and where you think it all ended.
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