iPhone from different country

If you purchase an unlocked phone, yes. However, the warranty is only valid in the country where the device is originally sold.

No. That is not true. There is no global warranty for iPhones.

Since different models are sold in different regions to support different LTE bands, it will probably never be true.

in principle yes, as long as the operator bands are same

check for this post:

https://www.apple.com/iphone/LTE/