"Why do they prohibit us from reading the books?"
Translation:Vì sao họ cấm chúng tôi đọc những quyển sách?
Normal native Vietnamese speakers would not normally say "cấm chúng tôi đọc những quyển sách" but instead "cấm chúng tôi đọc sách"
Yes, I noticed vietnamese speakers often drop the "cây" too when referring to one item. e.g. cây bút (pen) is referred to as bút. I often wondered if saying cây bút would sound as awkward (to the listener) as saying "please may I borrow a pen thing". Of course, in English, saying "I had apple after dinner", would sound horrible (and leave the listener wondering if it was one apple, or many apples) compared to "I had AN apple after dinner".
no, "cái" is a general classifier while "cây", as a classifier, is used in three situations: for plants; for stick-like objects; and for musical instruments, mostly string instruments.