Things only move from one phase to another by physical means. If energy is added (like increasing the temperature or increasing pressure) or if energy is taken away (like freezing something or decreasing pressure) you have created a physical change. =)) Hope it can help!
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A better equation would be dE=dm*c2 showing that a change in mass is equivalent to a change in energy
This is possible because the order of the addends does not matter. For example, 3+8 is the same as 8+3. No matter how you list the addends, the sum will always be the same.
because of the change of state of matter
The simple answer to this would be no. Density is the mass per volume of a substance so if you were to add either one of these quantities the other would have to rise by a proportional amount and the density would remain constant. However this become untrue when the amount of matter you are dealing with become on the order of a planetary mass. This much matter will produce a gravitational field which will cause pressures to result that will be enough to invoke a phase change in the portions from the center of the mass on outwards. In this case the density will change with the change in phase.