一、答案：
4. when 或 on which
1. when 或 on which
2. which 或 that 或 不填
3. when 或 on which
二、解释：
1. 如果是the day作为定语从句所修饰的先行词,则其后的定语从句的关系词一般分为两类情况.
1）如果定语从句中缺少the day去做它的主语/宾语时,则只需要填入关系代词which/that,而且如果做宾语,也可以省略不填关系代词.
2）如果定语从句中缺少on the day去做它的时间状语时,则需要填入关系副词when或on which(= on the day).
2. 原因很简单：
1）关系代词which/that就是代替先行词the day,在定语从句中充当主语/宾语的.
即第二题：(which/that) I spent with you in the countryside
= I spent which/that with you in the countryside
= I spent the day with you in the countryside
2）关系副词when = 介词on + 关系代词which = 介词on + 先行词the day,在定语从句中充当时间状语.
即：
第四题：when the old scientist took us to the lab for the first time
= on which the old scientist took us to the lab for the first time
= the old scientist took us to the lab for the first time on which
= the old scientist took us to the lab for the first time on the day
第一题：when we first met
= on which we first met
= we first met on which
= we first met on the day
第三题：when I first came to the school
= on which I first came to the school
= I first came to the school on which
= I first came to the school on the day