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-bloods 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".