Can I buy an iPhone in the US and use it in another country?

So a sister of mine lives in Colorado, and for black Friday might be buying me an iPhone 5S or 5C, and mailing it to me in Mexico. I don't really care if it's locked, as for now I'll only be using it as an iPod touch until I go back to the US in a few months. I would go for the newest iPod touch, but it's slow compared to the newer iPhones. So Id rather get a 5S for the same price with better features.
I don't want to get it unlocked as either iPhones would be too expensive, and I won't be using it as a phone here. But I'm not quite sure what can be done about the contract, whether there's a way around that, and not having to pay for it. Since it would be pointless for my sister or I to pay each month, if the phone won't work here.
Hope someone can answer my question ^^ And also, no I won't buy an iPhone here. They're just too expensive.

Why can I not always receive iMessages on my iPhone?

After I updated my iPhone to ios 7 I'm not receiving iMessages until I get back home or put 3G on. Before messages would automatically turn to sms text messages if one person doesn't have Wi-Fi. This means I'm not receiving important messages until I get back home and it is too late. And my phone also doesn't receive pictures unless I put 3G on. So if I randomly put 3G on I get pictures from months ago. Does anyone know how to fix this?

Added (1). I already have iMessage and SMS checked off in my settings and it still isn't working.

Added (2). If you don't understand the question please don't be rude and say I don't know what I'm talking about. IMessage needs Wi-Fi.

Is iphone 5 still available for sale?

I want a iphone 5 for Christmas but I have been looking at koodo (my provider) and Apple but neither of the sites have the iphone 5 on them. They have the 4s and then the 5s and 5c. So I was wondering if they are still selling it or not or if you could get it in stores?

I have an iphone that's translating things to polish and I can't stop it?

I've already made sure my language is set to english, and i've restarted, but that isn't helping. At first I noticed in Viber, that some of the msgs I were getting were garbled up… But it turns out my iphone is translating, all the msgs i get, into polish… Or at least I think. Now I'm starting to notice it with other things too… I don't know how to stop it or even how to figure out what's causing it.

Added (1). My keyboard is fine and the txt msgs i send are in english… My only issue is the msgs I receive.

What does 'line rental' mean for mobiles?

I have been looking around and various different 24 month contracts for an iphone 4s.
I have found some good deals for, say £20.60 a month but with ' £29 line rental '. What does this mean? Will I need to pay more that £20.60 monthly for my phone?

Why won't my speakers play my iphone 5 music?

So I brought a docking system for my iphone 4 last year which played music through and charged my iphone 4 fine but then I upgraded to a iphone 5 and I brought one of these: http://www.mobilefun.co.uk/genuine-apple-lightning-to-30-pin-converter-p36240.htm to put onto the docking system so that I could play music through my iphone 5 but it won't play my music but it will charge it. It comes up as "this cable or accessory is not certified and may not work reliably with this iPhone" but I don't see why, is there anything I can do?