Nope. Only the character on the run earns the XP.
My highest character is the Mage at level 4 who just completed the #4 dungeon. It looks like the layout of each dungeon remains the same each time you enter it, but the location and type of treasures are random (not sure about the type of monsters, since I wasn’t looking out for that). Each time you enter a dungeon, a wheel is spun to determine the dungeon effect; some are good, some are bad. So far, I’ve run across common, uncommon, and (what I believe is) rare (since it has a blue outline) items.
While in a dungeon, your character can walk across multiple tiles at a time, but doesn’t auto-path around hazards, which is annoying. Once you get within range of a monster, turn-based combat kicks in, although you are free to attack at range while out of engagement range. On your turn, you can move X tiles (determined by the character class) and take one action (attack or use an item) in either order. Taking the action, though, ends your turn immediately.
There are six types of damage (Physical, Fire, Air, Water, Earth, and Void) with each weapon doing damage of one type. When damage is dealt, the amount and type is displayed as floating text above the character/monster. Each character has their default attack plus class skills that are unlocked as you progress through the dungeons (I think). Skills gain experience and levels. And once a skill levels, it looks like you have to spend gems of the associated damage type to upgrade it. So it’s looking pretty grindy.
It’s a little too early for me to pass judgement. But I will say that I was enamored with Book of Demons at this same point in gameplay time. I’m not, yet, with this game. We’ll see how the dungeons open up, what variety of items and skills there are, etc. I will say the second dungeon is much larger than the first, so we’ll see. It uses the Unity engine, as an FYI.
One last thing: it’s lacking some basic QoL features, but I’m hoping they’ll be added.