His experience as a mature businessman, and aged adult six decades of living, told him something terrible was going to happen.
"Aged" (pronounced, in this context, with two syllables!) implies very, very old, like one of those Georgians who lives to be 135 by eating yogurt every day. A self-respecting 63-year-old like Peter wouldn't think of himself with this word, especially not in the era of Viagra -- he'd be like, "I'm sixty-three years young, dammit!"

One of the soldiers was approaching the gate (or: "the fence"?), laughing, to the wicket hauling a young woman -- scarcely more than almost a girl -- as she tried trying to break free.
I assume that by "wicket," you mean either забор ("fence") or ворота ("gate")? Nowadays, "wicket" usually refers either to the wooden targets used in cricket, or to the arches used in croquet (the croquet-wickets made from playing cards are called воротца in my Russian edition of "Алиса в стране чудес"!). Anyway, the original word-order "to the wicket/fence/gate hauling" is impossible; the other changes are only style-suggestions.

Peter had never had served in the Army military, he wasn’t a special forces police SWAT officer, he wasn’t a martial arts master either. But he had grown up in a tough suburban district blue-collar suburb and all his childhood and youth went he'd been in endless fights with other terrors like him.
Definitely switch the order of "never" and "had"!

Special forces, in US English, generally refers to elite, highly-trained divisions of the military, such as Army "Rangers" and Navy "Seals." But I assume you're talking about a special division of the civilian police, so the acronym SWAT would be the correct term here.

And, of course, "to swat" is what one does to cockroaches and other obnoxious bugs: "fly-swatter" = хлопушка для мух. Also, to an American (even a civilian), the word "army" excludes the Marines, the Navy, and the Air Force -- it just means "the U.S. Army," which is only one branch of the American armed forces. So Peter would more likely use the non-specific term "military" instead -- but maybe he'd say "army."

"Suburb" sounds more colloquially American than "suburban district," and "blue-collar" suggests that it was a rather rough place, even if not as bad as "the inner city."

Later, in his life as a businessman, it helped him a lot, in business because the contemporary business world obeys follows (or "works by", or "proceeds according to") the same cruel rules. Life is the best teacher and life in the district that neighborhood made him learn the rules very well. He drew in had internalized a few basic concepts: like always fight back, never surrender, never or hit from behind.
Except for the mandatory "the" before "contemporary business world," the above changes are merely style suggestions.

But I don't like the word "obeys" here, because it sounds too respectful for the context. Again, using "district" in this context doesn't sound very American, so I recommend "neighborhood" instead. And I would definitely repeat the word "never," because no-surrendering and no-hitting-from-behind are two entirely different rules. (God didn't say "Thou shalt not kill or steal or commit adultery" in just one commandment!)

He found a couple of pretty crappy knives -- they were pretty crappy, but the quality of thesteel didn't matter...

"Pretty crappy" sounds great to me; only the word-order needed slight adjustment. (To improve the "sentence rhythm" -- it wasn't so much a problem of grammar.)

Peter found a place out of the view of both the guy and the girl, lest she could give him out away to the guy with a sudden gaze behind the guy's his back.
"lest she give him away" -- note that there's no -s at the end of "give," even though it's 3rd-person-singular, because "lest" requires a subjunctive verb after it. You could also say "so that she wouldn't give him away." In either case, changing the word-order to "with a sudden gaze behind the guy's back" avoids the ambiguity of "his" (Peter's, or the German's?)

He caught an appropriate moment, jumped on the guy would-be rapist, covered his mouth with a hand, yanked the guy’s jaw up to open expose the neck and slit it open, still holding him tight in a tight grip with both hands, and legs crossed round the guy’s waist, until the blood fountain from the open severed vein ran dry and the shudders of the guy German subsided to trembles.
"To open the neck" really must be changed to "expose" -- and I took out the "and" between "hands" and "legs" because otherwise it gives the impression that Peter has four arms (two of which are cutting the man's throat, while at the same time the other two are crossed around the man's waist, along with the legs!). The other edits are purely about style, however.

(And, by the way, arteries spurt blood in "fountains" more than veins do, you know. Then again, I've never slit anyone's throat. I suppose the jugular vein would produce quite a fountain, while a severed carotid artery would become an absolute GEYSER of blood!)

Also, you are overusing the word "guy" a bit. "Fellow" can be a neutral synonym for "guy", especially from someone Peter's age -- "he watched the fellow ripping the clothes off the woman" sounds natural and colloquial to me, for example.

"Thug" or "scumbag" are appropriate to describe a Nazi who's doing something bad, like raping a woman (but perhaps not when he's innocently smoking a cigarette, or whatever.) As ruder synonyms for "thug," you might occasionally use "bastard" and "son-of-a-bitch" (or "S.O.B."). They're relatively mild vulgarities (especially in 2014, but even in 1941 they fell short of "мат"), and to me they sound appropriate for the "internal narrative voice" of a respectable 63-year-old American gentleman. However, reserve any hardcore obscenities -- such as "motherfucking Nazi cocksucker" -- for Peter to scream in rage during a one-on-one fight (if you use them at all!)))))