Why didn't the housekeeper...[Spoile rs]

I'm not sure that she removed the bullets from the gun to deliberately put Joyce in danger. I think she took them out as a precaution due to the insanity angle - should Joyce be driven to insanity she would probably end up doing herself harm so if she finds the gun then there's a chance she could kill herself whilst of unsound mind. So Miss Lu, no doubt knowing more than she lets on, takes the bullets out as a way of saving her new mistress from an untimely end by her own hand. In a similar way, if a third party looking to kill Joyce should come across the gun then once again the removal of the bullets could be an indication of attempting to save rather than putting her at deliberate risk. Just a thought!

Did she give it away or just let her continue to run the place?

The woman did eventually save her life in a way by shooting the guy trying to kill her for the inheritance. I myself thought the housekeeper was plotting to get the inheritance too and the bullets thing is curious. Not really explained; comes off as a red herring. Maybe though the housekeeper wanted to kill the other guy all along & though the heroine would somehow interfere. Or, the gun might be taken by someone else. It's a bit unclear.

I suppose that yet another view of Miss Lu might be taken. She may have been acting crafty rather than mad.

She could have been pretending with all that spooky spirit stuff to scare away the family. She then gets to keep the family mansion to do with what she will.