Neighbourhood

We have horrible neighbors.. they are one of those who act they are sweetest on your face but then do something really ill on your back. We share walls. They first used to create problems by either closing our washroom pipelines since it goes from their area and then connects to the main road. This time we were having construction/renovation in our house and they filed a complaint with the local authority regarding construction noise. We had everything passed with MDDA but now since they are now on inspection we have to fill a fine. I don't understand for what. They did all sort of construction and what not we were never one of those bothering them.. infact since we share walls and their house is on height we had all the construction material falling, but not even once we complain just because we are neighbors and it is obvious if we share walls this will happen. I would like you to help me with two things here: 1. Please tell us what we can do regarding fine? We haven't done really anything wrong then why are we liable to pay 2 Their staircase to their servant quarter touches our wall and person climbing those stairs can peek through our house. Which is a cause of privacy? 3. They have a problem with our dog like they have asked us strictly not to let out dog our after 10 because of the dog barking at night. In winter it was okay, but in summer she really likes to stay out. And if we keep her out they scare us that they would complain in fact they are so insane that if we go on our vacation and leave our dog out.. they said they would get her picked up by complaining to PETA organization or local animal concern NGO or something.. But we have our friends who visit our place every day in specific intervals to feed our dog and everything. We are really panicked and we are so scared to leave the dog that we stopped going out. It's really difficult to get mental peace when you have such neighbors. We are always terrified of what will they do next. I really hope to get help from you on this matter. Thank you in advance!