Is there a JSON scheme for a JSON scheme? In my application, the user can load their JSON schema, and I would like to check if it is a valid JSON schema.
Yes. This is a meta-scheme of the JSON Schema draft-04. You can use it to validate the JSON schema.
Yes - It is recommended that schemas refer to the schema that they implement by declaring the "$schema" property. At the time of writing, this is most often "http://json-schema.org/draft-04/schema#"
"$schema"
"http://json-schema.org/draft-04/schema#"
See https://spacetelescope.imtqy.com/understanding-json-schema/reference/schema.html for a discussion of the $ schema keyword.