Конечно, вот перевод ваших предложений на английский язык с указанием способов перевода аббревиатур и сокращений:
I immediately realized that I had miscalculated when I made a turn, because there was a traffic police car (ГАИ — Госавтоинспекция, State Traffic Police) ahead of me. (Перевод Аббревиатуры: ГАИ — State Traffic Police)
The diligent student Lenka was planning to drop out of school and enter a vocational school (ПТУ — профессионально-техническое училище, Vocational Technical School). Her son started loafing and skipping classes, paying no attention to anyone’s words or threats. (Перевод Аббревиатуры: ПТУ — Vocational Technical School)
But when in Moscow they said "GUM, Duma, and the Taganka Theatre" (то есть — meaning "sights for visitors" or "tourist attractions"), then, recalling Hamlet’s words, one had to turn “their eyes into the soul” (- “Thou turn'st mine eyes into my very soul”). (Фраза из Гамлета — "Thou turn'st mine eyes into my very soul")
Will the Security Council (Совбез — Советы Безопасности, Security Council) participate in reforming the law enforcement system? — Most likely, yes. (Перевод Аббревиатуры: Совбез — Security Council)
It is heartening that my father’s efforts were not in vain — now that girl, who once wept by the university fence, is already a doctor of sciences, professor, and teaches at Moscow State University (МГУ — Московский государственный университет, Moscow State University). (Перевод Аббревиатуры: МГУ — Moscow State University)
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