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Yes a bucket of a mixture of small ice pellets, say a few millimeter size, plus water, (this bucket being enveloped with some insulation) would be a great zero degrees Celsius reference point.
if you want something more precise you can read this :
https://en.m.wikipedia.org/wiki/Celsius
isotopic distribution of heavy and light elements in water also has a very slight effect on melting point. So, rainwater and water distilled from ocean will not melt at the (exact) same temperature.
See : Vienna Standard Mean Ocean Water https://en.m.wikipedia.org/wiki/Vienna_Standard_Mean_Ocean_Water
Now, about small particle fusing together this is true not only of ice but of any material.
it's called sintering and it is caused by diffusion and a lowering of the surface energy.