Welcome to the forum. 
Hardcore is available from the start, it’s not a higher difficulty thing. You just have to choose hardcore when you make a new character. They’ll be golden in the character selection screen.
Not for new characters, but you can get them for alts
Also with v1.2 you now unlock both Elite and Ultimate when you kill Loghorrean in the Necropolis on Normal difficulty.
Game should have to reinstall the DLC once you enable it again so if that doesn’t happen try unticking and then ticking the box again.