can somebody tell me in pure english how I can rewrite the following sentence or paragraph?

Your sentence just needs a bit of adjustment:

“I lowered the window of the carriage and looked back to see my father growing smaller and smaller as the train pulled away from the platform.”

The phrase about the father growing smaller and smaller is metaphorical, not implying that the father is actually shrinking, but that he appears to become smaller in the distance. It’s fine to use. The word “growing” means “becoming,” as in “growing frightened.” It doesn’t mean “getting bigger.”

I lowered the window of the carriage to see my father get smaller and smaller in the distance as the train pulled away from the platform, ..

As the train pulled away from the platform, I lowered the window of the carriage. I looked back and saw my father appear to grow smaller and smaller as the train left the station.

I agree that It should be two sentences and that you should use the phrase train pulled away in both sentences or in one. growing is certainly the wrong wording.

As the train pulled away from the platform I lowered the window of the carriage and as I looked back towards my father he seemed to shrink in size as the train pulled away.

( sorry Ti’s the best I can do without a rewrite)

As the train pulled away from the platform, i lowered the window in the carriage and looked out, i watched my father fade from view as the train moved along the track.

No & don’t use the phrase, “as the train pulled away” more than once in the same sentence.

Maybe say: (2 sentences)

As the train pulled away from the platform, I lowered the window & glanced back.

My father seemingly became smaller & smaller.

I stepped into the carriage and waited for the train to go. Slowly, it began to pull away as I opened the window slightly. I looked back, only to see my father fading away as the train continued to move.

What that particular sentence is saying is that that the father isn’t shrinking. He just seems to grow smaller because you’re moving away from him.

. . . .and saw my father disappearing in the distance as the train pulled away.

Grow smaller? Now that is a brain teaser. It could stand that way. I once read somewhere where a woman’s diamond necklace dripped like a waterfall. Or, a man’s determination was likened to that of unyielding steel.

and saw my father as the distance parted us he was becoming evanescent to the world, becoming smaller and smaller with every passing moment when the train pulled away.

If you were going to be picky then you could re-phrase it as the “and looked back and saw the image of my father grow smaller and smaller”. This implies what you were seeing was getting smaller and not the physical state of your father getting smaller.