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2

Yes - you can have a state where increasing the pressure would create a supercritical fluid See Phase Diagram


4

Many places, and especially in everyday life, metals are defined by examples and descriptions of their properties. In physics(solid state physics) metals are defined by the Fermi level within an electronic band. I do not see anything that makes copper special from other metals in this sense.


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The term you are looking for is premelting or "surface melting." It is an observed phenomenon (which could explain how ice skating works) with some thermodynamic descriptions. Basically what happens is the system is separated into two distinct phases, a solid (ice) and a vapor (air). There is a surface energy associated with this interface. If it happens ...


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In other words, for, say, an elemental solid, should we expect a portion of its surface to be liquid at any given time, with this portion increasing steadily until the melting point when the whole thing becomes liquid? It is possible for many compounds be part solid and part liquid under the right conditions. As ice melts, you have this condition. ...



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