I've played slightly more than a dozen times, but I've only gotten to floor 8 or so, so these are mostly impressions of the earlier levels. I know its early on in development so you're probably aware of most of this, but having a second point of view is helpful never the less!
-The matrix item mechanic is my favorite (the one that gives stats and a prefix along with a few random abilities of a certain sphere), but usually I only find one or two by the time I start getting into dangerous encounters (around floor 5). I would love it if you got a matrix everytime your summoner leveled up. The level ups are rare enough to balance this out, but it could be every other level up as well. It would also be nice if you could choose an ability to pass down when using the matrix. Currently I feel like I should wait to pass their abilities on before sacrificing, although that may be intentional.
-I like the starting options. I think each 'class' should have one default ability along with the other three chosen abilities to distinguish them more. It would also be cool if your starting demon got a semi random (or chosen) prefix buff, so to make him more unique.
-It would be cool if some demons could grow or evolve somehow. Not like Pokemon, but logical evolution. You could find equipment for a skeleton and turn him into an armored skeleton for example. Or let your slime eat something magical to get a different kind of slime. Or maybe theres a baby dragon thats weak early on but has higher growth rate than other demons (imo it shouldn't tell you its a baby as your character wouldn't know, but could imply that it grows in the flavor text).
-I would like to see the negotiation system touched up a little. It seems weird that the slime is smart enough to demand things for example! Surely you could just offer him three health stones, or alot of hp without waiting for him to ask for them? I've failed just because he would only demand sacrifices. Also when other demons ask for items in general you should be able to say "how about this other item". It just seems like the basic demons should be easier to negotiate with, as they aren't as smart or experienced.
-Some combinations seem too strong. Like getting the lightning passive +50% to shock with good AoE lightning skills. I ran into three prefixed lightning birds that had lightning breath and it was guaranteed death as they move very fast. Stacking dodge also seems to quickly get out of hand very fast. Things like giving the Willo Wisp the Goblin's dodge passives.
-I would like to be able to back up with my demons into choke points, and be able to run without having to unsummon everything. Currently I need to waste 6 turns if I need to reposition. It makes me think that going around with everything unsummoned is the smarter way to play!
-Currently it seems like you're reliant on finding demons that fit your playstyle. I found almost nothing but the demon that cleanses and gives sp to others for one floor and nothing but two types the next. This is even worse because you can only have one of each demon type. Maybe you should be able to fuse two demons to get a random demon of the same rarity or floor? Just so theres something you can do if RNG is not going your way.
-You can't run from most fights unless you get the movement speed passive. This practically makes it mandatory as there doesn't seem to be any escape items. You can just let some demons die, but doing that is very costly and will make you too weak if you do it more than once or twice.
-I was expecting to be able to summon things as you're a summoner. There could be a risky summoning ability that summons random demons that may go berserk and is particularly dangerous to use on later floors!
-The 'low profile' passive either doesn't work right, or the text implies that it does something other than what it actually does. I assumed that it let you fire through allies so that you could stand behind your demons and fire non directed ranged attacks, but in practice the only use is if they are on the other side of the enemy your firing at and hes in your line of fire.