"That is right, you know."
I don't speak russian, but I can imagine your confusion. I thought of an explanation, I hope it's not too roundabout. When an english sentence ends with "you know", it generally implies that the speaker is trying to emphasize what he has said, because it is something that the listener should definitely learn/keep in mind. My example: "Don't poke the flames with your finger! Fire is hot, you know!"
I believe よ(yo) is used when you already know that you are correct in saying your statement, kind of like a rhetorical question in English. ね(ne) is used when you are essentially asking the person to either agree or disagree with what you're saying. (yo example in English) The movies is over there you know. (ne example in English) The movies is over there, right?
よ is when you are giving the listener new information. It's something the speaker knew already but the listener didn't ("the report is due tomorrow"). ね is when you think the listener agrees with what you are saying. This can be something they have feelings about ("the report was difficult, right?") or something you both already knew ("the report is due tomorrow, right?"). They can also be combined into よね. This article gives more of an explanation: https://www.wasabi-jpn.com/japanese-grammar/sentence-ending-particles/
yes, but it has a feminine tone to it. This goes back to when だ was considered "male speech", women would avoid using it in casual settings, so instead of saying そうだよ they would say そうよ。These connotations still exist to a lesser degree in modern Japanese. I think that right now、そうよ is also common between men, but is good to know the connotations that it can bring to the table.