Trying to figure out what carriers my iPhone 5 is compatible with

Question

Hi everyone.
I recently bought a new iPhone 5 (not 5c, not 5s, just 5). No SIM card. It was activated, as in I could access the home screen. I can no longer do this, as I was advised to restore it in order to unlock it, which did not work.
I went to both MetroPCS and T Mobile and attempted to load their respective SIM cards. In both cases the phone gave the error message "SIM card is not valid" which as I understand means the phone is locked to some other carrier.
Before I tried to restore the phone, I looked in the settings. I do not recall which row this information was under, but the text was "T Mobile 15.0". Clicking this led me to some 6 or 7 digit number, and clicking again led to an email, something something @ sprintpcs . com. I was under the impression that the phone was locked to T Mobile due to what I just mentioned, but clearly that was not the case since T Mobile SIM did not work.
I called Apple and the first person I was directed to told me he could not provide me with any information about the status of the lock. I asked to be connected to a supervisor, and he told me that the phone is locked to Sprint.
I am going to a Sprint store tomorrow to see what they can tell me, but I am confused about something.
Sprint Nextel US runs CDMA iPhones, which as far as I know, do not use a SIM card. However, my iPhone has a SIM card slot. The back of the box tells me that the phone is compatible with CDMA bands 800/1900/2100MHz *and* GSM/Edge 850/900/1800/1900 *and* LTE 1/3/5/13/25.
If I understand correctly, this means that if the phone were hypothetically unlocked, then it could be activated with any carrier, CDMA using such as Sprint, or with a SIM card from T Mobile, MetroPCS, AT&T, or some other. That is the the first question; if the phone was unlocked, could it be used with any carrier, GSM or CDMA, SIM card or no, with no problem? I have read in some places that a US CDMA phone only works with GSM *outside* of the US.
Second question. If Sprint will not unlock the phone, can I get a contract with Virgin Mobile, as a wholly-owned Sprint subsidiary?
Third question. The phone is still under what seems to be "hardware warranty". IMEI checkers confirm that it is under some kind of warranty until June 24, 2014. Does this warranty only cover hardware problems, so for example, if the lightning port was broken/blocked and I could not charge the phone? Or does it also mean I can return or replace the phone?
All the info I have on the phone is listed below.
iPhone 5 White 16GB
US
MD657LL/A
Possibly locked to Sprint Nextel
Possibly compatible with CDMA *and* GSM
iOS 7 or above (not sure)
Was activated at one point, is no longer activated
TMobile, MetroPCS SIM cards *do not work*
A1429

Answer 1

I have the same problem i have iPhone 5s and is lock on Sprint and i update on 7.1.1 and not restore and when the update was complet then i go to settings and write on carrier T-mobile Mk and then i put sim card from tmobile the phone is still locked and then i restore the phone and now i`m stuck on activation screen i need to put sprint card...
I`m from macedonia and i buy the phone from usa ... Sprint is only in usa i dont have sprint in Macedonia...
LOL