Can I say 様々な国から来ます or 異なった国から来ます instead of 様々な異なった国から来ます? Why is there a verb in between an adjective and a noun?

Can I say 様々な国から来ます or 異なった国から来ます instead of 様々な異なった国から来ます?
Why is there a verb in between an adjective and a noun?

様々な国から来ます is also fine. 異なった (which functions as an adjective) is used to emphasize the fact that the countries they come from are very different from each other.

You could think of the difference this way:
お客様は様々な国から来ます=The customers come from various countries.
お客様は様々な異なった国から来ます=The customers come from various different countries