If пиво is neuter, why does its form change in this case (accusative if I am not mistaken)?
This is genitive used in the sense of "partitive". This is the way to say "some beer" rather than "the beer".
What's wrong with:
Ты хочешь немного пива?
Is it wrong if I put the object before the verb? "Ты пива хочешь?"
This word order is also fine.
Ok cool. It currently marks that response as wrong. Thanks!
What about хотите ли пиво?, would that be correct?