You'll be fine. ASD is kept very much in the public eye.
Is there a fast pass for someone with ASD? I can't say Ive ever come across one and its somewhere we would go for the weekend 3 or 4 times a year with my now adult son. You can get round the problem though with regard to a water park if you stayed at the Jumeirah Beach Hotel. They open the water park very early in the morning for hotel guests only and we found we could get round everything a few times before the gates opened to the public. But we'd also go at other times and that was also Ok.
Problems at the airport? I can't recall any but then my sons disability is very obvious and we were always taken out of immigration queues and given assistance. But that said I doubt you'd queue up for long in the airport anyway, they really are prepared for passengers.
Ski Dubai, my son wanted to go and play in the snow park and I was a bit wary so I called up the day before and spoke to the Manager who arranged for my son to enter half an hour before the snow park opened to the public. He had a lovely time with his sister and by the time the half hour was up he was ready to leave.
The Malls are huge and there's loads for children to do and if you chose your timings carefully, as soon as it opens, you could be in Mirdiff City Centre for example and find only half a dozen people in the play area. In fact there's a smashing childrens activity there that's sensory related and thats never very busy, in fact when I was in Dubai a few weeks ago for a medical appointment it was empty all the times I passed early in the day. Mirdiff City Centre is also calmer and quieter than other malls.
Parks - there are huge parks all over the place for children to run around in.
The fireworks and fountains at Dubai Mall? Plenty of open spaces as well as restaurants around it where you can sit on the balcony and see everything.
Burj Khalifa - you would prebook a slot anyway and that cuts down on queuing up.
And don't forget Dubai is very child orientated so your DS would be treated very well anyway just because he's a child.
I think you'd be fine but please remember you are taking your son into the unknown and you have to accept there may be disappointments happen that would happen anywhere, not just in Dubai.