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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.

Vow and take a well. The con with an ant.
Either will do. But no half-blood will I stand.

Likely refers to the y that got removed. It's not a vowel (vow... well) or consonant (con...ant), but a "half-blood".