帮忙分析一下句子的语法错误好吗

第一句没有语法错误.
第二句：learn (from [而不是 on]) books."but"这个三转折词没有必要,因为前后文没有转折的意思.
第三句：Only 应改为 Only after；on the books 应改为 from the books; only after...can...是个固定的句型,中间无需用逗号分开.最后,被动语气we are known用错了.所以,这句话应该这么说：
Only after we test what we learn from the books can we really know what we have learned.