Hm. Yes, talk to the landlord and let the landlord know you're not turning off the light. I would also let the landlord know that your neighbor is being very loud.

Be polite to your neighbor if they speak to you again, but firmly let them know it's NOT you, and would they kindly please stop talking to others saying its you because you can hear everything they're saying. Also, I would ask them to please kindly tone down their voices, because you can hear everything and it makes your dogs bark, and thank you. Be polite, but firm with your boundaries.