If you listen to what Talana said to you when you first enter the Mine-gate, you know you can better leave this place and store it for later
This is a place you can do later when you can transform in dragonform (after you have your Battle Tower!) and the Black Rings in the Mine Tower are Level 28 or L 29 !! So I think impossible to rescue William from the Black Rings before you at least level 24 or 25 (?).
Going in the Mine is neccesary for solving the Main Quest I believe (for having the "Sigil").
But failing the quest "A Guild without a master" isn't a drama. You still can enter the Mine and find what you're looking for
If William got killed, I believe the key is lying on the floor in top of the Mine Tower
(but not sure about the right place
you can find William's key)