8、One day, he walked into an expensive shop after having been caught in a particularly heavy shower.
be caught in：突然遇到/碰上
Ex:
be caught in a heavy shower
be caught in a heavy snow
be caught in a heavy storm

9、He wanted to buy a $300 watch for his wife, but he was in such a bedraggled condition that an assistant refused to serve him.
in such a condition/state：处于一种状态
bedraggled condition：拖泥带水的状态
such...that.. ... ...：如此...以至于...

10、The assistant asked him to leave, but Dickie paid no attention to him and requested to see the manager.
pay no attention to him= ignore him=take no notice of him=turn a deaf ear to him= refuse to listen to him
request：求见（正式，礼貌，语气强烈）新东方新概念

Ex:
I requested the headmaster.