Probably not Autism and ADHD yes but ssi is hard to get under the best of circumstances still I would apply anyway if that's what you need to do. Separation anxiety not a chance and even with the ADHD you will probably get turned down.
Uhm I believe so my brother in law recieved SSI for ADHD but I don't know if it varies from state to state. My son recieves it for Autism and ADHD so best advice would be to just go get the forms and have dr fill them out and apply. Chances are they will require you to take them to one of their specialists for further testing but thats no biggie I had to do that with my son.