1,The girl ran into the room,SINGING.要加逗号 表示一边跑一边唱
2,AFTER teaching the class,he wanted to have a rest.After doing sth固定搭配,
3,Having BEEN beaten twice,the naughty boy was afraid to face his father.been被打了,而不是打了
4,JUDGING from her looking,she seemed very old.Judging from sth 固定搭配 这里looking也不对 外貌要用looks（你没看错要用复数）,貌似没有judged from这种用法
5,After SEEING you,I know you are a learned person.这个基本语法
6,"You can't catch me."Jack shouted,RUNNING away.跟第一题一样.
7,We hurried to the bus station,only TO FIND the bus had left.hurry to do sth,前后一致.