Unlock iPhone 5 legally for use abroad with Verizon? Calls with Verizon abroad

I'm not a permanent resident of the US but I'm going to buy an iPhone 5 from Verizon with a 2 year contract.
The problem is that I will have to go back to my home country in Europe in 10 months. I would like to know, therefore, if I can call Verizon during my contract to ask them to unlock the phone. Is that possible?

2nd question: since I decided to take a 2 year contract, it means that I would like to use my phone with Verizon abroad, meaning use my US sim card in Europe (because even when I'm back in my country, I will be paying $80 for the phone in the US, so I will have to use the credit there, otherwise it's a waste of money). I will mainly call the US from Europe. Will I be able to use my phone plan abroad?

I hope I was clear because it's a bit hard to explain.

Added (1). EDIT: If I decide to buy an unlocked smartphone, does it mean that i can take any straight talk card when I'm the US? I mean a SIM card with a US number attached to it (just like prepaid phones)

Verizon iPhone 5 comes SIM unlocked so you can use with any GSM carrier worldwide. You can use it in Europe with European SIM without any issue. You can't move your plan to Europe, you've to cancel the contract when you leave US and you're not returning for a long time.