I'm half Norwegian and I'm pretty sure that it can't be used intransitively. I could be wrong as I don't use Norwegian as my daily language (my father taught it to me but I live in Finland so Finnish is my day to day language). If you want to have the Norwegian equivalent of "to drop" (intransitive), I would go with the word "å falle ".
I am afraid it is not correct. If it were to be what you say, it would be Søster mistet egget i gulvet. However this does not sound correct or natural Norwegian. I say this accordng to what THAson has said somewhere else:
- "Using the indefinite and without a possessive for family is normally used for older family members (mor, far, bestefar, sometimes tante, onkel) but rarely for siblings."