Be polite but don't let your neighbour in your house.
My mum in law had similar problems in a terraced council bungalow. Neighbour on one side said she was using her washing machine and drilling in the middle of the night. This neighbour even contacted the timid neighbour on the other side of mum, to moan about her noisy nights.
Timid neighbour too frightened to disagree, this went one for a few months, with mum becoming increasingly distressed, and stuck in the middle. I remember her sobbing and showing me nasty notes pushed through her door. Anyway, to get to the point, the council fitted noise monitoring equipment in mums house..... Of course it revealed no noise! Still,the complaints from the neighbours came, nasty notes and phone calls. In the end the neighbours were advised by the council if there were any more complaints they may have to vacate their bungalows.
Having read all the posts, I think it may well have been a mental health issue, or tinnitus.