同意一楼的关于你的问题中的错误和第一句的解答
至于第二句,先行词the day在定语从句中作状语,其引导词有三种方式表达:
1. I will never forget the day when you dumped me.
2. I will never forget the day on which you dumped me.
3. I will never forget the day you dumped me. (即省去引导词)
于此有相似用法的先行词还有way. 如
The way in which he did it scared me to death.
= The way he did it scared me to death.
先纠正你that是关系代词而不是先行词
先行词指被定语从句修饰的名词、代词
第一个句子中 the day是做spent的宾语 所以连词that可以省略
第二句同理
不