A little "You Won" pops up if you beat ten fights, but they're all identical until I get around to adding different types of enemies. That will probably come in the next update or two.
Healing made more sense as a downtime ability from a game design perspective, but it doesn't make a ton of sense in-context. The first bit of story in the game might be a lore explanation for why it can't be done in combat.
More information (numbers included) are going to be in soon, that's been a common feedback.
Thanks for playing.