Help me correctly use error bars on Monte Carlo simulations -- 2

Job ID: 34248640

Budget: $10 – $30 USD

I'm working on a personal software project doing Monte Carlo simulations, and I want to estimate the accuracy of my simulations so I can correctly plot error bars. I have been reading a lot and think I understand how to do it with pass/fail tests, but then I also want to calculate error bars for another type of simulation that involves bounded results between 0 and 1 (examples in attachments), which I don't understand how to do.

1. Help me decide between confidence intervals vs credible intervals vs standard error vs standard deviation etc for the error bars.
2. I will explain how I'm calculating confidence intervals for pass/fail tests and you can tell me if I'm using them correctly.
3. Help me calculate error bars for tests with results between [0, 1]
4. Help me calculate error bars for metrics that involve differences and quotients of the type in #3 (Cauchy distributions?? ?)