New iPhone in Armenia

That would depend if Armenia's carriers support eSIMs. the USA model does not use SIMS.

I would not recommend doing it. If you bought it in the USA, the warranty would only be valid there. Buy it in the country you are going to use it in.

Only if the provider in Armenia supports eSIM (Very unlikely but check). That phone is dual eSIM only.

If you live in Armenia you will have no Apple Support or warranty on it.