I did my PhD on (malicious) visual impersonation of domain names using many of the techniques described here. There are many references to other visual doppelganger techniques included in my paper here: https://par.nsf.gov/servlets/purl/10256904
My research focused solely on the .com domain name space, so our character set was limited.
Essentially A-Z, 0-9, and the - character, and domain names can not start with the dash character.