Hello, I am a solicitor with 20 years experience. I will try to help you with this.
It sounds like he may well be responsible in law for the cost of repairing the damage he has caused.
Are you neighbouring terraced houses? The image I have is of some guttering extending from his roof gutter in open space then ending and water coming out of the end aimed for you guttering but missing in part. Is that right?
Ok he seems quite clearly to be responsible in both negligence and nuisance for what he is doing to your house. He cannot simply divert water from his roof onto your property, unless this has happened for 20 years or he has a specific right to do so. Any damage caused he should pay to fix. Is he aware of this problem?
Yes but perhaps best to nicely point out the problems to your house and that they seem to be caused by what he has done and that you would like him to fix the guttering. It might be worth getting a price for fixing the damaged wall as you may need to decide whether the damage to your relationship with your neighbour is worth it.