I am going to Europe and I wanted to know if my plan has an international plan?
No Republic plan includes calling from overseas on cellular. All plans allow you to use the phone on unrestricted wifi, just as you would at home, for calls/texts to the US/Canada.
If you have one of the legacy phones (Moto X1, X2, G1, G3, E1 or E2) the phone is unable to be used with any foreign carrier. If on the other hand you have a newer phone, you could swap the SIM with a local carrier SIM in order to gain local cellular coverage.
I can get text messages from Iraq but not able to send text messages to Iraq. Does this sound correct?
Yes, Republic does NOT provide outbound calling/texting to anything but US/Canada numbers.
If two phones are US numbers, but the phones are in Greece, will they be able to text one another?
The phones don’t know where the phone is located. All that matters is the fact that it is a US number. Of course, if these are Republic phones they’ll only have service whole on wifi when outside the US.