Having a battle aspect is fine, but why no healing? Any miss fucks you up later as you have no way to heal up and I searched all I could to find if there was any

You can heal when you jump on the water near your house. You can also get infinite money by interacting with the well in the town, you can buy weapons and armor that make the game way easier.

Personally, for the narrative, I rather not buy anything and keep it as it is. I don't need healing, and Ike's so weak he can't afford to fight every enemy so he just has to evade them.

Also, always use physical attacks. You always start fights with full stamina, and you recover much of it in every turn.