请帮我分析几个关于情态动词英语题

请帮我分析几个关于情态动词英语题
1.She walked fast in order that she____with the others.
A.may catch up
B.might catch up
C.could have caught up
D.might have caught up
这题为什么B呢?请帮我详细分析一下.
2.The teacher said that we would have one day off tomorrow,so we ____go to school tomorrow.
A.can't
B.mustn't
C.needn't
D.shouldn't
老师说我们有一天会离开学校,所以我们明天不用上学.是这样翻译的吗?为什么选择C呢?请帮我翻译句子.也给我讲解一下,谢谢.
3.It is usually warm in my hometown in March,but it ___be rather cold some times.
A.must
B.can
C.should
D.world
为什么选择B?帮我翻译并讲解这个句子.在这里,rather 是什么意思?