Phase Voltage Confusion
As you pointed out, the value you computed is one of the line currents, as you took the line voltage and divided by the load impedance.

The phase current will actually consist of the difference between two line currents. I believe this diagram can make it clear to you. Note that
\$I_1 = I_{12} - I_{31}\$




  Why is the phase voltage equal to the line voltage?
  
  My other question is, is the phase voltage defined to be something else if we don't connect a 3 phase voltage source to it?


I agree this can be confusing.

A phase voltage is a voltage measured across any one component.

The diagram I presented you has a phase voltage for the source and a phase voltage for the load. The phase voltage for the load is actually the line voltage. In a \$\Delta\$ connection, the phase voltage is the same as the line voltage. That is not true for a Wye connection. At the diagram, the voltage across the top impedance \$Z\Delta\$ equals \$I_{12}Z\Delta\$, which is clearly the line voltage.

The phase voltage definition doesn't change, but the voltage you are gonna consider does. You can't just assume the phase voltage is always the voltage between phase to ground, as this is not true for a \$\Delta\$ connection. However, this does not depend on having a 3-phase source connected or not, it simply depends on the given connection.