Okay - so this is how it works (please do feel free to ask questions if it gets confusing - it initially is a bit confusing!)
1. Set up a Google Voice Number
2. Buy around $10 or so worth of Google Voice calling credits (all you need - calling through GV is extremely cheap!)
3. Download GooveIP, a Voice-over-IP app (make calls through Wi-Fi. Premium can make calls through a data connection too - highly recommended)
4. Go to the other nation and buy a SIM
With that setup, you can call anywhere in the world with GrooveIP using data or Wi-Fi and the receiver will get your Google # showing up. They can call that number too, and as long as you have the GrooveIP [Premium] app open, it will ring your phone.
Now - here's an awesome glitch I found though. Although VoIP calling is nice, it certainly isn't the same exact quality as calling over a cellular connection. Remember how I mentioned I had a 100 minutes per talk per day? Well, if you know, Google Voice, if you use it to make calls, uses your normal minutes. What I found was that I could use those 100 minutes to call anywhere in the world as long as I had Google Voice set to make all calls (you can do that under the Google Voice settings).
I also found that I somehow received texts. Be careful though - as in some nations, that could cost extra. But remember - Google Voice can send texts through Wi-Fi, so if you ever want to text someone while abroad, use the Google Voice app to text them through a Wi-Fi connection. They will receive your text with your Google Voice number.
To answer your remaining questions:
International charges? Never, never use your American sim abroad. I always take mine out before arriving in the other country, or put my phone in Airplane mode until I can access a shop in the other nation to buy a sim card. They will rip you off like no other. Always buy a sim in another nation. (Its a cool souvenir too!)
Calls to the US for free? Will all that I mentioned above, if you use my glitch, I'm pretty sure there is no fee. With GrooveIP? Pretty sure there is a fee. But look at it this way - the cost of a call through Google Voice to the US is at 1?/min. That is laughably cheap. Here is a website if you want to look at calling rates with Google Voice:
https://www.google.com/voice/rates. You'd be hard pressed to find better calling rates to anywhere else.
Phew. That was a lot of information. I hope this helps though. Let me know if you need anything. You're certainly making me miss my Nexus 4 more though...It's been through quite a lot, and handled it wonderfully too!