they are glad Dasha hasn’t shared their destiny fate
Destiny is something foreordained - like 'your destiny is to kill Volandemort' (больше предназначение, нежели судьба).

to a gray-bearded aged man
Must he be a gray-bearded aged venerable Gandalf? Kolkhoz chiefs were usually men in mid-forties (fifties at the most) quite robust and vigorous. Nearly all of them were the members of the Party (important detail - not the leaders of the local Party cell - this position was usually occupied by someone else).

‘Who is it?’ he asked.
Robert may correct me if I'm wrong, but this sounds a bit impolite. 'Who is he?' would be more preferrable.

administrative building
Here, you can leave it as it is, but I think Ann should use some Russian words now and then. Say 'pravlenye' instead and let Peter ask about it.

Savinoff
Russian names ending with -off came from French (they needed to stress the ending consonant. And in writing only. English speakers do not need it). You don't need to stress pronunciation here, because in English both written names and said end with -ov, not -off.

the closest English equivalent for his name is Peter
Come on, they're the same things. Even an American can see that ;D

Ann said while they were striding towards the building virtually sensing heads turned in their direction
I just need a clarification - was it Ann who sensed that? What I mean - if you narrate from Peter's standpoint it should be Peter who would feel this. And if Peter noticed that it was indeed Ann who sensed it you should tell the readers how exactly he knew this.
And the other thing - how can anybody 'virtually' sense anything?

They came entered the house (which Ann called 'pravleniye') into a large room with a big table in the center and a handful of chairs around it.
Red tablecloth! There must be a red tablecloth on the table! And a decanter!


Here - look at the man in the center. He definitely doesn't look like Gandalf.

‘What are you going to do now, Peter?’
An amazing lack of curiosity again! How on Earth did you get here, Peter?

‘But…what will people say?’
It really should be Ann's concern. And Ann's proposal is really very VERY unbecoming for a village girl in 1941. And 'Gandalf' should object violently. Well, again, this is your story.

They went out of the building when the darkness started to dawn fade
Oh, I'm too lazy to re-read. Are you sure it was dark when they came in?

she had worked as a consular assistant in Great Britain for a long time before she retired
It's a fiction, of course, but her mom simply couldn't work there 'for a long time'. Great Britain officially acknowledged USSR in 1924. (16 years before the current events). Ann is twenty-something so she must have been born not long before that (1915-1919). Even if her mom miraculously happenned to work in UK (which is very doubtful) Ann should have spent her childhood in London. And more - even if somehow Ann hasn't been raised by her mother (say, she was left on her grandma) it seems very doubtful that a daughter of a dilpomatic official ended up in a Belorussian village as a simple teacher. No, I mean, really.
Alternatively, her mom could have been working in UK BEFORE the revolution. But this automatically makes Ann the member of the old-regime nobility. Her ma simply would not have returned to bolshevik's Russia from Britain after 1917.

Oh, a question of British style. British English required saying 'I/we shall' instead of 'I/we will' back then.

‘And that’s why you speak so good English your English is so good, I assume?’

‘Yes exactly, she has it on her fingertips.’
??? Who has what on her fingertips? And generally what are you trying to say here?

The house resembled the Nikolai’s one
(I'm not very sure about that. Ask Robert).

Peter felt like experienced a deja vu
then I entered the University
'I entered' is a bit official. And Ann did not belong to the generation of SMS writers. She would say university (In fact she woudn't even say "Универ" in Russia.
Oh, the other thing - there was ONLY ONE University in Moscow.

When I was a kid child and my parents were out for job I used to teach my little Kate how to count and write.
So, her ambassadorial parents were out of job... All things considered - they WERE serving the old regime.

‘The talk This conversation reminded me of my little sister,’ she said.
What are you going to be doing here during in the middle of the war?’
'During the war' doesn't sound righ somehow. Of course Peter might know that the war will last for a long time, but that 'during' implies they simply wait it out like a rain or a snowstorm.

I really hope the Germans won’t treat us very bad the Red Army will soon drive them out!
In that previous life of his he had no one who would truly love him
the new life was trying to give him everything he hadn’t had did not have back then
A question of personal preferrence I think, but let's ask Robert about this.

if we are doomed to die we will die together
either 'if we are doomed we will die together' or 'if we have to die we will die together'.

I didn’t feel so true and so happy I’m feeling now
Man, you're in the middle of the World War 2, you've just killed a man with a knife, cold-bloodily sliced his throat for the first time in your life and yet you feel happy. You're a maniac, Peter!

‘I love you too,’ her faint smile seemed to him glimmering brighter than the sun, ‘and I feel like I’ve loved you since the first day we met.
Which happenned only the day before yesterday, as I recall
O tempora, o mores!

I'll continue later. Please, consider removing so vast inconsitencies from the plot. Pleasepleaseplease.

Here, I found some pics you may find useful (note the radios, and also the fact that all women have their heads covered).