Neighbours Coconut tree leaves falling on our Car Shed Built

We have recently taken a Car and for which we have constructed a shed in front of our house, and now the the scene is my neighbors coconut trees leaves fell on our shed and causing loss to our steel Sheets placed as roof for the shed. If these were Cemented sheets they would have broken up because they are steel sheets they are getting too much dented and look very odd as they are hardly 1 year old and we have spent 20 k for the same My Neighbor has cut two coconut trees which was causing damage to thier property , but not the one which has causing damage to our shed I work in Bangalore in an IT firm and my mother stays alone in Goa where the issue is Wish to know my right on below points 1) I have asked them to cut down the tree but they say that tree is planted before the shed is Built and are very adamant to the cut the tree or replace the sheets? 2) Can i file a compliant in Village Panchayat, Police station and Ward Panch ? 3) What is the possibility that the tree can be cut ? 3) Can order can be passed as such they replace the dented sheets and cut the tree as well? 4) I cant travel frequently to Goa, if i file a compliant and be back to Bangalore for my Work will the proper action can be taken by the appropriate bodies in my absence as my MOM in illiterate ? 5) If no proper action is taken by the above bodies what can be my next course of action ? 6) Will hiring a lawyer and sending a notice will be much expensive ?