Ok, i'll try to answer some of your questions... but i've watched all 3 of the Japanese version too (original, sequel, and prequel), so my mind is a little muddled.
How did the kid know so much?
I'm not exactly sure to be honest... i think Samara linked with the kid because they were similar in same age, and were also distant from their mothers (that's why he called her Rachel)... so he was able to understand/sympathize with herr. Weak explanation, but i never really gave it much thought.
And why wasn't Rachel supposed to let the little girl go so the aden at the end said.
Because she really was evil.
And why did the horses kill themselves?
I think it drove her mad to live with the horses in the barn... also her dad loved horses more than her.
And what saves you from dying? Just copying the tape? Or copying then showing someone the tape?
Simply copying it didn't save you. You had to show it to another person. Samara wanted people to see what she went through, her suffering and torment, so she cursed it so that people had to show others her 'dream' or they would die.