Hello Blackout and welcome to the forums.
You pay only once, and there is no monthly fee.
The way DoF PvP and CoOp works - you are only matched against Armies and Town of the relatively same strength as your Army or Town.
So for example - if you have an army with 20 level 1 units, it will match you only against player of 17 to 23 level 1 units in the army. So it`s always a fair and fun battle, be it co-op quest, lay siege, town PvP or Army PvP.