It's not the weekend yet, some of us work on Friday afternoons! ;) I stopped being a student a little over 20 years ago....
The mass fraction of the phases should make sense, but check what you initialised with and then patched. I'd initialise the domain using "standard" and all being air. I'd then patch the two "solid" regions along with the temperature. The scale on the right is 0 to 0.5 which suggests something got mixed up: you may need to patch to "zero" and then "one" for materials.
For the mesh you want a smooth growth rate and low aspect ratio in the melt regions. You also want at least 5-10 cells across the melt region to capture the gradients.
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