My Comments in blue, corrections in orange

Just random writing

The passenger train to London just started moving.

(Good)

In a second-class smoking compartment 4 passengers sit, talking to each other.

(Good)

The man with the longest beard I have ever seen looks irritated, his flustered cheeks and widened nostrils say it all.

The A man with the longest beard I have ever seen looks irritated, his flustered flushed cheeks and widened nostrils say it all.

It sounds a bit more natural to not use "the" in this sentence, if you say "the man" you are implying maybe there are other men that have a variety of beard sizes :P

Also, the word "flustered" is a mental state, it's kind of a synonym for "confused".  If you mean that is cheeks are pink, then the word is flushed.

When I look to my right I can see the familliar surroundings change.

Good

I have never been away from the countryside.

Good

I am visiting my aunt.

Good

She has lived in London her whole life.

Good

Overall, quite good - you might try challenging yourself by trying some more complicated sentences, like maybe rearranging the last bit as:

"I'm visiting my aunt; she has lived in London her whole life, but I've never been away from the countryside."

Using longer sentences can make things feel a bit less choppy - don't go crazy with it, though :).  Also, while it is certainly ok to skip contractions when writing (I have = I've, I am = I'm) I would say that in everyday conversation, even at a professional level you are much more likely to use the contraction.

Again, really good job overall, jou Engels is geweldig.