Haha, thanks! I'm glad you're enjoying the game, and I hope you continue to enjoy what I have planned for the future!
As for your questions, Tanis covered it pretty thoroughly :) Just to add to the "battle stats" part of the question, though:
When you level up, only your HP and WP increase. To improve your other stats you will need to explore, construction certain buildings, do certain events, etc. Right now you can only increase your PHY and ARC by one extra point, both in The Glades, but many more opportunities will be added in future updates.
Same for recipes - they'll be found by exploring, through certain battles and story events, and so on. Right now there's only two, but more to come