Update! (cat keeps killing neighbour's chicks)
firstly I would like to thank everyone of you for your help. I had a good talk with the neighbour and I apologized thoroughly and even offered to pay for the damage but she refused and assured me that she holds no grudges against me which I'm thankful for. so yeah.
and we finally installed a net door and Nandu has been staying inside for two days. he wasn't happy for first few hours as he kept meowing alot and staring out of the door but we managed to distract him by playing with which at first he wasn't interested in. he is still not fully accustomed to this new setting but I'll manage.
About his neutering, we have pushed it for the next week as my cousin is visiting us and he offered to take us to the vet in his car so it won't be a hassle. hope everything go smoothly and Nandu gets comfortable!
all in all I'm ashamed for not looking into this matter previously but now I've learned my lesson and would rectify my mistakes for Nandu. thank you reddit for your help, I'm really really grateful❤️