If I buy an iPhone in Apple USA, will it work for me in Costa Rica? It comes unlocked??

You will need to get an unlocked phone from an Apple Store. The warranty will only be valid in the US. So, if you need any warranty service, you will need to return the phone to the US. And, yes, you should be able to use it.

Yes, if you don’t finance it through a carrier it will be unlocked and you can use it anywhere in the world. However, as kb1951 said, it will not have a warranty in Costa Rica. And you must have it shipped to an address in the US; Apple will not ship outside of the country where the phone is purchased.

Yes, you can get an unlocked phone through the website. If you want to get one from the US website, you need to be a resistant of the US with a US credit card. Apple does not ship internationally.