Hey palecur,
Sorry to hear you're having some troubles with our game's mechanics. I'll do my best to explain address them. For field cards, their effects can be found on the card when you go into your deck inventory. So if I click on a heal card and bring it into my deck, it tells me it bathes the player in light and heals the player. All the cards in the game should display these kinds of tool tips, and if they are not, please send me a screenshot and we'll look into what might be causing that.
Placing cards also triggers a short global cooldown, so players can't just play every card right away without any thought. Defense, magic, and attack cards each have a separate global cooldown, so you can play an attack card and immediately play a defense card, but you can't play two attack cards back to back without waiting a few seconds. Stronger cards can trigger longer global cooldowns, though those don't show up until later in the game.
The grids do change size periodically as you defeat enemies in long gauntlets or just from encounter to encounter. We were trying to really mimic that real time combat feeling, and one of the ways to do that was to vary encounters, kind of like how enemies in an RPG might dodge or parry.
As for the numbers, your goal is to get the ones in your attack area to zero while keeping the ones in your defense area as high as you can. Placing an attack card of 5 on an area with only 1 defense will do more damage than placing an attack card of 2 on an area with only 1 defense. The enemy player will be doing the same thing, attacking your weakest areas and defending their weakest. Once again, we were really trying to mimic that real time combat feeling. But actual numbers are all based on addition and subtraction.
It's best to try and widdle down multiple areas on any given grid so when the enemy defends one spot, you still have open places to attack and deal damage. And for most encounters in the first map, you can attack twice to every single time you need to defend. It feels pretty fast at first, but it's not quite as hectic as it looks! That comes later ;P
Hopefully this helps. If you have more issues, let us know and I'll do my best to answer them.