Waaaaaaay down at the end of the DBI perldoc it has a section "Database Handle Attributes" that shows the "published" attributes that are available for pulling out of the $dbh hashref. The first two items in your list are obtainable through the Name and Username keys (and there's a Driver that you can use to retrieve the database driver name the handle is using).

Update: Just to clarify I mean "published" in the sense of "it's explicitly documenting that the hashref for the handle will have those keys and it's implicitly OKing breaking encapsulation to retrieve them".