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So, if you're like me and you're used to the game mechanics of "Visit this NPC to raise this stat" or "Go to this place and perform this activity to raise this other stat" then the system can seem kinda weird, but as long as you play through the main story and do the girl's stories, you'll find your stats increasing as per story interactions either directly (as in "task completed, stat point gained) or by unlocking said interaction/location. So just go through the story normally and you'll find these opportunities (some of them, like Charisma and Physical, are *technically* available from the start or near the start, at least for the first few advancements). Looking at the stat scroll, they have little hints about how to get you started. I'll try to give non-spoiler info on it here for you :)

Charisma: Go to the bar in the morning and look around to find books, eventually you'll need to perform tasks for an NPC to raise it further (this is obvious and hard to miss so long as you keep visiting the bar in the morning).

Martial: Eventually you unlock the ability to visit a certain family member of yours, that'll deal with your Martial path pretty much in its entirety.

Insight: Once you unlock the ability to use the train station, use it and go to the Lake.

Magical: Go to the outskirts and start exploring, eventually you'll find somebody interesting...

Physical: Also outskirts, I hear working on a farm is pretty hard work. Once that's that, it might help to find somebody really strong to help you (requires advancement of story, it becomes pretty obvious once the character opens up).

In terms of recipes, unless I missed something, you only actually get ONE recipe in Act 3 just naturally (it depends on the meal you picked on Day 1, idk if the effect varies per food but I did salad and it's a pretty darn good recipe), but by exploring a certain district I know of at least one other recipe you can discover. Before Act III, I don't even think recipes are a thing.

Hope this helps you, friendo! ^-^

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

Thanks to you both!   Understanding the game just tends to make them all the better!  
Keep up the amazing work!   Obvious boner inducing characters aside, this is one great story!!  
Serious talent!  ^_^!!!!!