Home exemption/partial claim/new home purchase

I purchase my home 2021. I allowed my ex husband to claim the credits of the home or whatever it is called. This year I will like to include my home in the taxes but I have no idea how or what this results in. Do I get a higher return since I have a home? How exactly do I do this?

 

 

My exemption was approved, what exactly does this mean? I was told it protects my home if someone try’s to sue me. I just don’t understand this.