by the time of last term ,we have finish all the lessons

第一个句子【by the time of last term ,we have finish all the lessons】错误,正确的表达是：
By the time of last term ,we had finished all the lessons.
by the time of 表示“到...的时候”,句意是：在上个学期为止,我们已经学完了所有的课程.这里需要用过去完成时态,其结构是：had + 过去分词.过去完成时指：某一动作在过去某个时间或者动作之前发生,即发生的时间是“过去的过去”.有关过去完成时的定义、用法请参考：http://baike.baidu.com/view/201153.htm
第二个句子【we had invented many new things by the time of last years】,其实,也有一点小错误.正确的是：We had invented many new things by the time of last year.
这里的years不需加S.具体的解析请参考上面的.