Jacqueline, exhausted from a long day of travelling around the South Island

Jacqueline,
exhausted from a long day of travelling around the South Island, decided to
check into the Southern Alps Inn, Queenstown for the last three nights of her
stay in New Zealand, instead of her usual backpackers accommodation.
After
checking in, Jacqueline asked the front desk about her options for safety
regarding her property. During her travels, Jacqueline had accumulated quite a
lot of precious souvenirs, including rare jewels from India valued at $20,000
NZD. As she was ending her trip and flying back home to England, she wanted to
know that her souvenirs would be safe. The innkeeper made her aware that they
couldn’t keep anything at the front desk but that there was a safe in each
room, where her possessions would be completely safe. She placed her jewels,
plane ticket and wallet in the safe.
On the
last night, she took the money she needed and went downtown to enjoy some
relaxing festivities and to get some food. After eating, she came back to her
room exhausted, collapsing onto the bed to sleep. Her flight was early the next
morning, but when she woke up, she found the safe was still there but her
things were not. Not knowing exactly what to do, she rang the front desk
assistant. After twenty minutes of arguing with the front desk assistant, she
realized she was going to miss her plane. She called the police and left
without paying her bill, which was valued at $480.
Further
investigation by the police found that the safe was faulty and did not meet the
standards required to keep possessions safe. Two days later, cleaning staff
found an Indian stone and enamel box in the room, which was valued at $700 NZD.
The Southern Alps Inn manager said that the box could be sold and the proceeds
used to pay Jacqueline’s bill.

a)
Is the Southern Alps Inn liable for the rare jewels, wallet and
plane ticket held inside the safe?
b) Can Jacqueline claim from
the Southern Alps Inn and/or any other legal remedies?
c)
Did the Southern Alps Inn manager have the right to keep the Indian
stone and enamel box?