If there were a Tony Award for sheer, unadulterated chutzpah on Broadway, a man named Hershey Felder would win it hands down. The answer to the first, of course, is that anyone who has a half-million dollars or so gets on Broadway.
Money is the only passport needed.
One answer to the second is that famous people's estates definitely should be more diligent about guarding their legacies. Felder comes with no apologies for not being even an approximation of George Gershwin. Both parts, you understand. And a lot of it, believe it or not, is flat. Of course, most composers aren't particularly good singers, but they don't do one-man shows.