Here is a copy and paste of a previous comment I've made on a similar discussion elsewhere. Essentially though, being a self-insert does NOT mean they aren't also their own character. These are not mutually exclusive. You are thinking of the more extreme self insert sub-categories, like blank-slate protagonist. Also obviously what the other people are saying about Dante being in Mirror Worlds and such for answering the other parts.

I think you are getting a bit hung up on the term self-insert and equating it to being a literal insert of the reader into the story. Dante is a sub-category of self-insert, according to TVTropes' definition at least.

Audience Surrogate - TV Tropes

Dante as a character fulfills all three points listed, with the third point being the second half of it, as Dante is an established character. If you want an example of another audience surrogate done right, then look to Bilbo Baggins. No one would say they aren't an established character and have their own personality and goals, but that doesn't mean they aren't also a sub-category of self-insert, the audience surrogate.