If you want to reduce the sound from your flat, you can add acoustic or sound absorbing material under your carpet.
There are many options for different budgets (google sound reduction in upstairs flat)
In terms of improving your relationship with your downstairs neighbour, a really good first action would be to stop labelling him as mentally ill and start to consider that he may be very stressed and grumpy after prolonged noisy upstairs neighbours who don't take any notice of his complaints.
There's always two sides to one story, but this is completely solvable