Answer:
"Which"
1. The dog which barks all night belongs to Kate.
2. Mary wore the dress which she brought in Italy.
3. The cat which is chasing the laser belongs to me.
What
1. A family that prays together, stays together.
2. That green bag belongs to the teacher.
3. The homework that the teacher assigns is very easy.
Step-by-step explanation:
Which is used for animals in general or things, while, That can be used for people, animals or things.