I liked most of your translation. I think a few things should be different, and a few things puzzled me too, so I hope a native speaker will help out.

чужой in the second line means "strange" here, and the line is closer to "on this big, strange Earth".

in the 5th line череду means a sequence or a series

farther down, что-то тихо мне сказал=he said something softly to me

and I think, but am not sure that:
"поняла я, будто он всю жизнь меня искал"
= "which I took to mean that he had searched for me his whole life"

because, in your translation ("I understood, as if he had searched for me his whole life") how would his having searched for her his whole life help her to understand?

оборвалась счастья нить= the thread of happiness was broken