Do we have a list of what all types of credentials can be created and why it is necessary to have a public URL while creating these credentials?

No, currently there is not any list that formalizes to know if one schema already existed. Regarding why it needs to be public is due an issuer creates a credential based on a schema and then the user needs to go to a verifier to generate a proof, the schema needs to be discoverable in order to know how to pass it because the schema defines the rules and the structure of the credentials and the format that is public (the schema defines the fields like the date of birth and the format that they are).  Nevertheless, any PII is public, only the structure/skeleton of the schema where the credentials will be created.