I had to get some sleep...
The thing about the dungeon (I didn't give the name or description cause I didn't want to give it away) is that your characters have a stamina status (only discernable by a smiling or sad face). After a certain amount of time in the dungeon, they will become tired, and you are basically kind of screwed if all your party members are tired.
The AI is fairly predictable, they will heal if low on health, and makes full use of their available HP or SP for special skills. Whether or not that's a good thing is up for debate. You can issue command to them during dungeon crawling to split up and look for a teleporter out of the dungeon. If they are tired or low on health, there is a chance they will get in trouble if the party is split up.
I'm pretty sure every floor has a teleporter back to the entrance of the dungeon. Like duckroll said, it's completely random. Each floor is not big at all, but your characters gets tired rather quickly at the beginning of the game.
The whole leveling up experience is split between night time and day time. During the day time, you play a dating sim like framework with the main character to level up his personal stats. In the dungeon, you level up your persona through battles. You can combine and mix two or three personas to create new ones.
This game is definitely not your typical JRPG, it has alot of unique gameplay elements which may be a big turnoff for people. I personally think it's rather interesting thus far, although I'm not sure if I fully enjoy the day time elements. Seems like a chore. I also wish you can spend more time in the dungeon, but I'm sure that will be achievable as I progress.