Iīve found some examples that explain the use of that in cleft sentences.
Cleft sentences are emphatic sentences. They are used to give thematic and focal prominence to a particular element of a clause. Whenever a cleft sentence is used, there is a contrast implied.
A: Would you like to borrow this book?
B: No, itīs the other book that I want to read. [Itīs the other book, not that book, that I want to read]
A: Are you going to buy it?
B: Well itīs my wife that decides. [Itīs my wife, not me, that decides]
Itīs possible to derive four cleft sentences, each highlighting a particular element of the clause:
Subject as focus:
It was Sam who wore his best suit to the dance last night.
Direct object as focus:
It was his best suit that Sam wore to the dance last night.
Adverbial adjunct of time as focus:
It was last night that Sam wore his best suit to the dance.
Adverbial adjunct of place as focus:
It was to the dance that Sam wore his best suit.
Your sentences # 2 and 3 are correct. Sentence #4 sounds less common in written English since most of the examples use "who" when they focus on the subject. Itīd be interesting to read other opinions.