1 His mother told him that he (would) catch a bad cold if he (doesn`t) put on more clothes.
从句中时态不对.最好把would改成will,因为无论他妈妈现在告诉还是过去告诉他,从句中他不多穿衣服会得重感冒都是一个客观事实,不受主句told的过去时态影响.或者将doesn't改成didn't
2 Friendship helps us (understanding) who we are,why we need each other and what we can do for each other.
搭配不当,应该是help sb (to)do sth.help us understand
3 Would you please show me the English-Chinese dictionary you bought (it )last week?
这里有个定语从句 (that )you bought,此处省略关系代词that或which,在句中作宾语,所以不需要再用it了.