Do any United States of America phone carriers support the phone with 4g or LTE ??!?

All major carriers in the US support 4G and most places support LTE. The problem may lie in the fact that different countries use different radio frequencies for different things. A truly international phone will have the ability to utilize networks across the globs (they have more stuff in their guts). You need to check the specific model number to determine what it is capable of. Even though the phones may all be called Moto One Action does not mean they all have the same model number and capabilities from the radio standpoint.