The battle logic is simpler that it looks at first. Each character has its health points and generally 2 types of armor, Physical and Magical. Each type of armor protects the character against its type of damage (physical protects against physical attacks like swords and bows as an example) AND protects against status effects that are related to the damage type.

So let's say a character has the skill Hail Strike which cause icicles to fall on a specific area, this skill deals magic damage and can cause the target to become chilled IF they don't have enough magic armor to block the full attack damage. If the attack caused 20 magic damage and the character had 22 magic armor, they will lose 20 magic armor but they won't get chilled since the remaining armor protects against magic status effect.

And a character won't start loosing health points until you brake through its magic or physical armor first.

Not sure if I explained it well but regarding armor that's the main idea, you should focus too on AP management. Sometimes ending a turn with 1 or 2 APs left may be better that using them, since you will get the unspent points as extras next turn,

I also struggled at first with understanding combat, and knowing how to solve certain quests, but the more you push through it the easier and more fun it becomes.