A more elaborate explanation why I didn't use your suggestions:
appeared somehow here in Belarus Soviet Union, in 1941.
Gonna use it

and the immediate pain told him he wasn’t.
Gonna remove the 'immediate' and leave only "the pain".
The pain is because he knows the source of the pain.
I know that you know. It's Basics.
I'm definitely overusing the word 'immediate(ly)' -- trying to struggle with it.

village at moment and it’s about 70 miles over 100 km to Minsk
No way. It'll be miles. Peter is American and she just tried not to puzzle him with calculations.

hey have horses at least.
Yup but I don't think someone would lend him one. They'd find a thousand excuses instead.

the border frontline is in a stone’s throw
already explained

keep in mind that Peter KNOWS what would happen.
He doesn't. Explained. I don't believe in the overall knowledge. Sorry, but it's just that.

Considering the pre-war propaganda the oncoming war should have been swift and take place on enemy's territory.
Maybe. Maybe not. Maybe particularly true. Many people had connections with polish relatives, friends etc, and when the german troops were accumulating on the Polish territory, I'm sorry but I don't believe there weren't rumors about it.

‘What about you?’ Peter asked, ‘Look at those bombers, the Germans will be here within a week! You HAVE to leave immediately!’
Maybe. I'll think about it.

Always keep in mind that Peter knows what would soon happen. At least in general terms.
Ok, I'll try to stick with it wherever possible.

I will not evacuate leave at all I'm not going to leave
Peter used this word. Word used correctly. Why should she change it?

In the first days of the war there was total chaos
Someone smart would know that or at least could guess. I pretend that she was smart Just my choice.

in this weak little woman who was going to fight till the end
is the selected piece really necessary? Why? If someone else seconds your point I'll correct it right away.

while he, the a strong man
'the' is an exaggeration here. I think it's ok. If someone else tells me it reads bad, same story.

strong man the defender who supposed to be defending them
1. who was supposed...
2. the defender is another exaggeration
3. the "if someone else-thing".

‘Foreigners, heh! And just who the hell then I am?’ he thought,
Not sure it's better.

‘Why the God or whoever played this mean joke
I thought God could be referred either way, with or without the article. As a proper noun, like a name, or just like a noun. Like a job position.

Should I immediately run away now or should I stay
Great. Gonna use it. This 'immediately' again.

or should I stay and (try to) help these people?
Well, maybe. I'm not sure yet. Probably I'll use it as well.

Where would he run? Back into the woods? No transport - you said this yourself.
Yeah, right. I'm trying to make a point about him deciding if he wants to continue on the attempts to leave or not. Not to really "leave".

and prove something as atonement in redemption for (to redeem) my old life?
Not sure.

These were questions without answers. Peter virtually heard the sarcastic voice in his head:
These were -- I intentionally omitted them. "If someone else....you know"
the voice -- whose voice? He doesn't know that. He doesn't know the owner of the voice. Why 'the' then?

------

Sorta like that.