The correct answers are What he did was set the kitchen on fire. and What he did was to set the kitchen on fire.

When a wh-cleft sentence focuses on an action (using the verb do in the wh-clause), the focused element after the verb be must be an infinitive clause. You can use either a bare infinitive ("set") or a to-infinitive ("to set").

Gerunds ("setting") are incorrect here. Additionally, the wh-clause ("What he did") must use normal statement word order, not question word order ("What did he do"), and the linking verb was cannot be omitted.