Juries already do this, and they're pretty average folk in them.
There may be a jury at the lowest level court to find the right punishment. Even in those courts they don't entrust juries with the finding of fact. That's what the judge does. They don't trust juries with pretty much anything. Even in current society where there is such a thing as law. In your dream society, juries would give judgement based on how they are feeling that day.
Local gaols, private gaols and volunteer gaolers/private gaolers.
Who would volunteer to bee a jailkeeper? You? And why do you assume there to be such a thing as private jails, private jailers, or private property? And even if that were not a problem, how would people trade goods? By trading apples for oranges? Would they keep gold locked up in their house.
Better than now, so yes. Not tens of thousands of folk in gaol for victimless crimes.
How do you expect the average Joe to give fair and good verdicts in court if 99% of them don't even understand the merits of your anarchist utopia? You are basically modeling your justice system after Australian aboriginals or Native Americans.