Amendments to the story:

He was rambling through the forest, crouching through dense thickets, crossing small clearings and shallow creeks
weak little woman who was going to fight till the end for herself and for a handful of little kids
United States, ma’am,’ he replied, thinking to himself: ‘It looks like the interrogation is starting sooner than I expected. It had to happen sooner or later.’
‘I don’t think so,’ she said smiling, ‘as far as I know it’s Franklin D. Roosevelt, at least he was the President three months ago when I last saw your newspapers. I recently received a couple of issues from someone for my students.’
The old man said something to Ann
‘You are in the Soviet Union, Belarus, about 110 kilometers due North from Minsk,’ she said with a slight accent, 'it must be something around 70 miles if you prefer these units,' she added after a short pause.

‘The Soviet Union? I can't believe it,’ he said aloud, while thinking to himself: 'Did she really say Soviet Union?! Was she kidding? The Union joined his maker, uh, what's his name... Ahh, Lenin, more than a decade ago... One of us must have been gone off his nut'.

‘What’s wrong?’ she asked.
‘It’s not about my belief or disbelief,’ she said becoming serious, ‘I think you must know that; tomorrow you shall have to tell something to our district officer, and you better tell him something he would believe in, otherwise things might get very ugly.’

‘I gather that, miss,’ Peter said with a tired smile, 'I don't know how to prove it but I'm not an American spy sent here in the middle of nowhere to mouse out the up-to-the-minute methods to boost the production levels of your dairy cattle.'

'Umm, I'm not sure I understood you completely, but I think I got the point,' she added incredulously, 'mister "not-an-AMERICAN-spy"'.

'What are you trying to say? I'm neither an American spy, nor a Chinese spy, nor even an Uruguayan spy. I am not a spy at all,' Peter said, slightly irritated in tone.

‘Okay, It’s late now, you better get some sleep and tomorrow we will try to help you. I think our police will contact USA consulate in Minsk, if there is a consulate, and Mr. Roosevelt will help you out,’ Ann back-pedalled, a note of resignation in her voice.
‘Can you bring them with you when you come to see me tomorrow?’
I see,’ Peter said slowly as a thought struck his mind:
Nikolai took out of the old scarred cupboard
As far as I understand both scarred (with marks on skin) and battered (subjected to heavy repeated blows) impose some kind of physical impact. If the thing if falling apart for natural reasons: old, rotten, etc., what will it be?

Considering the bombers flying overhead, the border has got to be a stone’s throw away, the Germans can get here in a week or so. When are you going to evacuate?’
This is what the regular army should do, not you.
What if they DO treat the civilians bad?
then who the hell am I
‘Why did God or whoever else, who played this mean joke, stick me into this very place?’
There is not a single clock in this house
I saw comrade Somoff
Somoff? Who is that?
There were a dozen soldiers in the truck's bed with strange dated guns with drum magazines in their hands.
Throughout this whole paragraph, there should be a "the" before "sergeant," unless "Sergeant" (capitalized) is used as a title before a surname such as "Somoff."
ok

only by chance not tearing it off the old rusty hinges
seemingly still in a daze
It’s empty, get into it
Peter just grabbed her, lifted her up and slid her into the barrel
Wasn’t that barrel empty?
What was in there?
‘Mushrooms’, she said fixing up her hair. ‘Pickled.’
Agree

Okay, I'm done with Throbert's corrections, some of them were edited, some were applied 'as is' but anyway, that was just great!
Special thanks for detailed explanations!

P.S. Too tired to continue, will work through Ramil's tomorrow.