Italian Beehive Possibly Missing Queen

First Queen was out of her cage in three days, even though she was marked, never seen her in the frames after 2 weeks. They had Bur Cones in between three frames that looked like upside-down ice cream cones. Clean up all of the Bur Cone except for the two largest sides, thought I would kill too many bees removing it. Never seen the Queen, purchased one but she was unmarked. Haven't seen the new Queen. Looking for some ideas of what could be wrong or what I should be doing. Thanks