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The word is probably:

Semester.

The endless semen, not many polyester makes not me — the heart's duplicated of a studious half-year.

Seme(n)+polyester-poly(=many) gives semester, which is almost the word with the central letter e duplicated. Of course, "studious half-year " is what it means.

What comes after semi without individuality, I call the heart. Next, yes! Easter has come! Oh no...not in full. The very beginning's quite missing.

Semi-I(individuality)+(y)es+(eas)ter also yields the same word. The letter coming after sem(i), e is the heart, or the centre of the word.