不可以用what,因为它不是一个关系代词,但可以说：
1. is this school__the one that __you visited last week? 用而This school is the one.这个主句这样写是成立的.
2.is this school__that__you visited last week?直接用关系代词that引导先行词this school的定语从句.
这道题： is this company __-you paid a visit to the other day ? 不可以用 what ,理由同上题.