Alright, I played a little more (my batteries ran out before), when you attack the monster's labyrinth it uses the same battle system, but your units go through a maze-like dungeon. Both the dungeon and the town defense happen at the same time and you can switch back and forth between the battles (this all happens in real time).
You can visit the buildings that you defend during the day, and each one has a special function (there are a lot of games like this). You can invest in the buildings to level them up as well, but I'm way too early on to do any of that. After you are done setting up for battle, hiring people, equipping characters, etc. you can choose to go to the night phase, where the battles happen. In the morning you get a report on who leveled up, how much damage your buildings took, and get some money and 'free' experience that you can use to level up anyone you want. After that you get a choice of scenes you can watch, I'm not sure if they have any effect on the game, I think they are more just to flesh out the characters.
In the first full battle I did, 2 of my 3 buildings were destroyed (if all of them are destroyed you lose the game). I'm not sure if you can prevent this because there are way more enemies than you have units that early on, so if you're playing the game save the tavern because that lets you hire new characters. I haven't seen any counter for the number of (in-game) days I've played, so I don't think there's a time limit like some games (Atelier series).