Yes, of course aperson with autism can get a gun. There are no restrictions on autistic people when it comes to purchasing guns.
Anywhere where it is legal to own a gun - there are no restrictions on autistic people owning or operating guns.
There's no such thing as a mild form of Autism - a person is either Autistic or they're not, how they're effected can be mildly but this can change throughout their lives. There are no restrictions on Autistic people owning a gun, as long as they have the capacity for responsible gun ownership.
If there's any record of it, no.
An Autistic is a person with Autism.
A person does not 'develop' autism - a person is born autistic.
A person does not 'develop' autism - a person is born autistic.
A person does not develop autism. Autism is a neurological difference, as such it starts within the womb during the second trimester when the brain is being formed.
I'm going to guess, in the United States, no, not legally. One of the ineligible classes for owning a gun is defined as: any person/people "adjudicated as mental defectives or incompetents or those committed to any mental institution." I don't enough about Autism to define it, but I suspect it falls into that category. As long as you have a gun permit then you can have a gun. And you can have autism.
Someone who is born on the autism spectrum/has autism spectrum disorder/is autistic. Often used in an offensive manner towards autistic people.
The eyes of a person with autism look the same as the eyes of other people.
A person does not develop autism, autism is not something that occurs to neurotypical people, in the same way that a white person doesn't develop into another race. A person is born autistic, their brains form in the womb.
A teenager doesn't develop autism - a person is autistic from birth.
Autism can be inherited from parents with genes for autism. Autism can also be the result of the spontaneous mutation of a gene. It is suspected that a person with the genes for autism might need an environmental factor (in the womb or shortly after birth) to trigger the development of autism.