Blue Badge - advice needed

I am waiting for the outcome of my application for a blue badge on behalf of my 9-year-old son. His severe sensory issues make journeys very challenging and often quite dangerous, but as we live in central London we decided to sell our car 3 years ago as it was expensive, rarely used and of little benefit for him as we could never park close to our destination anyway. We now rely on expensive taxis and the generosity of friends to drive us about. If we do buy another car it will be 100% for his benefit as we don't need one for any other reason.

I was wondering if anyone has managed to get a blue badge for an autistic child under the new hidden disabilities criteria? As my son gets the middle tier of the care component of DLA but not the mobility component does anyone know if he will also qualify for a reduction or exception for car tax if he gets a blue badge? I was also wondering if we bought an older (cheaper) car for him if the new ULEZ charge will apply or will he qualify for the exemption until 2025 for blue badge holders?