Lets say I'm at my refresh phase, and I have removed all focus tokens from my unit cards. If I want to attack again with my unit cards, do I have to pay for them again utilizing the focus tokens and the objective cards?

In other words, are the unit cards free to play every round after I have payed for them once before?

You only pay resources when you play the card. Once a Unit is in play, it remains in play until it takes enough damage to be destroyed or another card causes it to leave play.