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.