Answer:
"Which"
1. The dog <em>which</em> barks all night belongs to Kate.
2. Mary wore the dress <em>which</em> 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.
Explanation:
<u>Which</u> is used for animals in general or things, while, That can be used for people, animals or things.