How do you deal with dangerous monsters? Escape to next floor immediately? Retreat to heal and try again (probably with consumables this time)? Retreat to heal and carefully explore trying to not meet the group again? Something else?
It depends on the situation. I'll dive (rise?) to the next floor immediately if I end up surrounded and would lose a demon/myself trying to run away, or even if it's just some insane unique like Charliss or Antoria. If I won't incur any losses, but still can't take on the enemies even under favorable conditions and with consumables, I'll retreat using my demons as a distraction, and then give a wide berth around the pack/summoner/hero while exploring. Otherwise just run, heal up, and try again, this time leading them to a better position and using consumables.
What do you do when you meet a new group? Read all its abilities and decide either to fight or escape? Or try fighting anyway? Do you use swiftness/dash to retreat and change which of your demons are deployed?
Definitely read all the abilities and stats of unknown demons and even modified demons, they could have an ability that exploits a huge gap in your defenses (such as a type weakness found in most of your party, or maybe some kind of status that you don't have the means to heal, like lacking calm vs. panic attacks). If my character/party is really strong overall I'll probably fight anyway. But the biggest thing that will help you survive in Demon is just walking away and never looking back, seriously, especially since demons won't try to track you down like enemies would do in some other games. And yes, swiftness is amazing for running away. Just be careful when exploring after running so you won't end up surrounded by packs of enemies you can't take on.
Another big thing that gets me killed is putting my demons' lives above my character's life. There will always be other demons later, and you can even revive lost demon's, but you can't revive yourself! So try to place your character's safety first