Questions about DP Quests

Hello, guys, I have started playing this game not that long ago, and I enjoy it a lot. I was doing some DP quests to unlock the next stage (Dracula's Castle) and got stuck on some of them. I've read a guide here on Reddit but didn't find anything useful.

The first batch of quests is in Lost Temple where I need to obtain Lord of Elemental's Heart. I've done multiple runs, but I am facing Fire Elemental's portal only. Is there a way to make other elemental's portal to spawn more favorable or is it after specific floor or something?

The second batch is in Ancient Arena. I need to get items from 8 rare enemies which spawn in lounges. I am using Bandit and Kaito in order to steal items but my problem is encountering them. I have done 7 runs today, up to floor 75 but can't find them. I even used PoE twice in most of these runs but no luck. Is there any way to S/L and get those enemies or is there a point of going further than 30 floors to find that lounge? I found Wizard of Oz and the other party once and it was before floor 30.

Lastly, I am interested in the Hidden Gumball (Ghost Captain). Do I have to get gems in order for him to spawn, or getting crystals is enough to encounter him?

Sorry for lots of text, but I wanted to make myself clear.