I know that cortana will be available to US first and later to other regions ...What are the other parts that will be similar ??? Also , if I change my region to US what problems will I face ( if any ) ??
If you don't have Xbox music available in your country that will probably stay the same. Other than that, the rest should be exactly the same. The only difference that may occur is down to hardware limitations of the different phones.
I believe the only issue you may run across if you change your region to the US is downloading apps.