Umseting - Kinesiskt einfalt-Enskt - "双子星" 天上的星星数不清 最亮的是你 不管有多远我愿意 放弃一切寻找你 ...

I am not English expert, but may I suggest?

"give up on" without "on"
"two hearts who" changed into "two hearts that"
"No need that time shall prove to me " changed to "I don't need testimony by time"

Small alterations to an almost-perfect translation:
---
"Twin Stars"

Among the uncountable stars in the sky
You are the brightest one
No matter how far you are
I want to give up everything to follow you

I don't need time to prove to me
That it's certainly true
Because I know your joys and pains
I can feel them all
We are like twin stars

We are in the sky facing each other
A linking thread between us in the dark night

The two of us can live only together
Two hearts
Who have the same belief.
---
Anyway, a very good translation overall!

Ian, I see your mother tongue is English. I thought that "facing each other" means more like "having something in contradictory", am I wrong?
"That's certainly true/Because I know your joys and pain": I don't think it is like this because there is that "keyi", so it is "I can surely know..." , what do you think?

Hi Oana,
In English, "opposing each other" would mean "disagreeing about something," but "facing each other" would simply mean "standing/sitting/being face to face (e.g. usually looking at each other?)."

As for the second part, I was connecting it to its previous line, but maybe you're right; that it should be connected to the line following it...?
Hmmm...I don't understand that part of the lyrics very well...

Thank you, Ian