I don't know how much had already been corrected by PM - and I didn't want to break up the flow of the story
So here are some musings of an Ole Woman on the Neverending Story...

Be warned: this is looooooooooooooooooong.....

The morning was cloudy when he locked the door and went by his usual way to the bookstore. It started to drizzle. Unfortunately, "it" wasn't the clouds, but a dog standing on the roof overhead. Suddenly he remembered that today is Friday
I agree with translations.nm.ru: "Suddenly he remembered that it was Friday"– would be the correct option here. If the sentence starts in the past, I’m afraid you have to keep it there And “Suddenly he remembered that today it was Friday" sounds weird: you can’t use “today” in the past.


, and decided to drink some beer after work. He couldn't explain why such a strange thought had come to his mind so suddenly in the bookstore. He stood in the middle of the store, gazing at the shelves when the door bell rang behind his back. He turned round and couldn't believe his eyes. It was his father he hadn't seen for ages!
"Dimitry, my son!" the old man cried. His face was wet with tears of joy.
"Where have you been for so many years?" mumbled Dimitry , hardly moving his lips. Then they both stood silently just watching each other - the father and the son.
"Stop, catched!"
??? I’m unsure where this comes from – but I’ve never heard it before. I have only ever heard a director yell “Cut!” – or “OK, Cut”, if he is eloquent…

shouted the director, "Wonderful! wonderful! You have never played like this before!"
The film was about a man, that
“a man that” is used, I suppose – but I don’t think it’s totally grammatically correct. I’d say “a man, who”. Men are usually animate (although I know a few exceptions )

had found treasures, hidden by his father-pirate, and the most interesting thing was that the story had been based on the real events!
Again, to me it would sound more natural to say:
…had been based on real events!
…had been based on facts!

Having thought for a few seconds, the director decided to shoot another take: Take 2!
"No way!" Dimitry said in a disappointed tone, "I shan't say a word before I get my coffee!!"
(he must be related to me somehow…)
"Alright," said the director, knowing that if he didn't allow Dimitry to have a cup of coffee, Dimitry wouldn't be able to act as well as he had a few minutes before. He tried to put down one crazy thought that sprang into his mind: Arsenic in the cup.
"Why, why this damn director so hates me?
Why, why does this damn director hate me so (much)?
(always auxiliary verb in questions )

I never pretend to be a Bradd Pit...but I`m not so bad at all!"- thinking Dimitry,
…not so bad at all!"- thought Dimitry,
or
…not so bad at all!"- Dimitry thought,

heading to nearby cafe.
to a nearby cafe (any cafe, not specified)
or
to the nearby cafe (known by all the members of the crew)



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