I left a bottle of water in the fridge for the past three months. I took it out today. There was a block of ice in it. How?
The piping for refrigerant circulation is in the fridge walls, so obviously it's colder near the back as there is no heat from the front door reaching that area and heat exchange with compressor/coolant circuit is at maximum.

As for the partially frozen water, this happens to mineral water and water containing any salts in general. As water freezes out, the salinity increases, resulting in freezing point depression for remaining solution. These processes are the basis for fractional freezing.