what is the function of "už" here? Does the sentence work without it?
Ty knihy už nikdy číst nebudu. = 'I will never read those books again.'
Ty knihy nikdy číst nebudu. = 'I will never read those books.'
Would the sentence work with 'zase' instead of 'už'?
no, it would mean that it will again happen that you won't be reading them. You normally read them, but this weekend again, you won't. Or something similar.