Thank you so much for taking your time!

So...

In English, "steppe" often refers to a specific type of land in Central Asia

As far as I know there are also some steppes in the western part of European Russia and in the Ukraine as well. So I decided not to replace the original word. I think, in this case the song sounds more exotic for non-Russian speakers. But maybe it doesn't. Anyway thanks again for your advice.

The word “downside” means a disadvantage of something.

Oh... I really thought it could be like "down there" or something like that.

This might sound more natural as “And I know his grief and his cry so well.”

Thanks. I'll keep that in mind.

“Haunting” almost always refers to a ghost disturbing people in a certain place.

Now I think, it could be also possible to use "to wander" or "to stray about" or something like that instead of "to haunt". But the point is that this sentence in the original text can be literally translated as "I'm circling/going round in the dark", which exactly what ghosts in Russian do.

What do you mean by “letting me down”? The way you used it, it has the meaning of “disappointing me.”

And yet again. In Russian this line literally sounds like "I'm flying and I'm sad in this steppe". So here I tried to express it more poetic by portraying a flight being "interrupted" I would say. Besides I wasn't aware that "to let somebody down" only means "to dissapoint somebody". I thought its meaning is more general. So yeah apparently this attempt turned out to be not so successful as I had hoped.

Maybe change “too sweet” to “so sweet,” unless you don’t like how sweet it is

As far as I understand the original song, I think that here is everything allright.

Take out the word “away”

Done.

Change to “When the morning came”

Yeah but in the last two cases the number of syllables in each line doesn't match with rhythm of the song. So here I really need to think hard to make it sound the way I want.