"You practice cooking rice."
Translation:Bạn luyện tập nấu cơm.
'Nấu ăn" can only be used when it stands alone. For instance:
You cook=Bạn nấu ăn
However, if there's complement after "cook", it must be "nấu"
You cook chicken=Bạn nấu gà (not Bạn nấu ăn gà)
ăn = eat. Nấu ăn = cook to eat. In another work, cook for the purpose of consumption. Nấu cơm = cook rice. So you can see squeezing ăn into the middle of it would be weird because now it means "cook to eat rice." You can however says "nấu cơm ăn" = cook rice to eat. But if you practice, then you just practice cooking, not eating too :-)
ấy is a third-person marker that's usually with one of the personal titles (e.g. cô, anh, ông) to create 'he' or 'she.' Bạn is second-person (you) or 'friend,' so I'm not sure how or why you'd put the two together. Bạn stands on its own here.