Good job on the first four lines.
"биться" doesn't mean "to be beaten". It is either "to fight" or "to beat" (as in "the heart is beating"). The word has other meanings too, but I don't think any of those would apply here
And I didn't even know how much I loved the rain.
I may be hairsplitting, but I'd say "Your grey name is rain"
Gibberish. These lines are ungrammatical, so we can only guess about their precise meaning. My guess is: If I could only know the time of our meeting and divine by hands (?) now much time is left for me to breath. But I wouldn't bet a penny that this is what the lyrics author had in mind.
So, once and for all...
"And I didn't even know" (or "I never knew", whichever you like better)Я и не знала...
And even I don’t know...
"A glance of the faces that are running away" or "turned-away glance of running faces". This is not a good English, I know, but it isn't a good Russian either.Взгляд прочь бегущих лиц
You don’t look at others running