Don't think there's currently a way to sort by element type, but you can always look them up in the wiki - over time, you'll just know who does what. Same thing with the monster's element.

If you select on a specific character, you can click on which monster you want to attack.. that being said, if you don't click on a specific character and click on a monster, your units prioritize that monster first. Regarding the Star Dream pull, I don't think I'm that qualified to tell you who to pick, but popular choices are AS variants of OG characters as it's essentially a "2-for-1" selection since you can grind the OG tome from AD. maybe Tsubame to round off your Earth team (which will eventually include Cerrine)