"The system of justice is pretty much a perversion of the ethical norms, so many things are kind of a bit obsolete nowadays. But, what is a shocking thing, the law still operates under those assumptions.
If it is some non-violent crime or some literary ridiculous nuisance, any normal person would vote not guilty, pay a fee, move on, but no."

Right, there are ridiculous non-crime "crimes" like drug use. If the jury was instructed to interpret the laws as they're written, then even a blockchain juror system wouldn't fix this. Because they'd efficiently interpret things, and be like "ya he did smoke pot, so therefore, X". The only solution here is to have a society and court who don't believe these things are criminal acts.

"But, are they actually in the safe environment? Are they influenced by somebody else?
Are they anonymous? That should be even better. But, how much anonymity can they have?"

These are good questions and I don't necessarily know the answer. I think you easily could have anonymity, if that seemed like the best way to do it. Your juror account could be just some account, and at first you have no history and build history over time.

I'd imagine it would also be possible to make it so jurors are publicly known and linked to a real identity (a thumbprint or whatever) but your specific decisions are hashed and not known.

Of course, there can be different blockchains with different specs and we see which one proves to be the most trusted.