There are a lot of titled players with high functioning autism.
One known is GM David Navara, but there are others. It is discused if Bobby Fischer was Asperger too. There was a buzzing Magnus Carlsen was autistic too, but looks false acording to Quora. Another example of GM that looks to be autistic is GM Julio Granda from Peru.
As for Down Syndrome, they ...
OK, welcome to chess.stackexchange. First off with such FIDE questions need to bear in mind their "golden rule":
The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. Where cases are not precisely regulated by an Article of the Laws, it should be possible to reach a correct ...
“When you see a good move, look for a better one”.
Of course blitz is different, but you were playing with a 10 second increment and with no time hurries. Any excuse why you didn't take some time to calculate the checkmates.
It depends on the exact time control and type.
I went straight from zip to 1750 USCF by playing weekly at the club in their lightning tournaments. Every 10 seconds a buzzer or bell rings and you have to move immediately.
Games looked more like movies. You had enough time to plan decently and to make your move. They taught a lot more than playing one slow ...