I'm hoping this improves...

[Skandranon]

As to the second point there, there was no coordination.  After we clear a room, and start healing up, I'd be all, "Okay, next let's go this way, through this door I'm facing."  (Naturally, I'd walk up to the door to emphasize.  Although now I think that it would be easier to just use east or north or whatever.)  They'd be all, "Sure, okay."  But when everybody gets up, I'd go off in the direction I'd indicated, they'd go off in another direction, I'd rush back to them, and we'd get swarmed by two rooms worth of mobs.

People like this don't grasp even the basics of the game. Groups like this will be rare, but they exist. If it happens, I'd get out of the group and go looking for another one. A tank isn't strictly necessary for non-instance elite quests, but to live without one needs at least a baseline level of coordination.

so I rush to the middle of the three, Frost Nova

Wait, what? You what? Why...why did you do that?

I mean this as a more general question, really. I see a lot of beginner mages doing this and it completely puzzles me each time it happens. The freeze time won't be long enough to be anywhere near useful and the damage is minimal at best. Frost Nova generates extra aggro above and beyond the damage, so it's not a good move in any group situation.

For your case, let me share this advice: if your group is badly coordinated, AoE options are the first to go off the table. It isn't your fault. Bad groups happen, and what happens with bad groups can't be called your fault. That said, there are things that you can do that minimize the Bad Stuff that happens with bad groups, and it's a good idea to learn what those things are.

Anyway, do higher level players learn how to better go slowly through a dungeon, draw enemies more efficiently, and actually help out their party members?

It's not usually a function of level. I've found good, competent players and stupid brain-leaking idiots at all levels of play so far. It may be hard to get into a group, but don't stick with a really bad one. It isn't worth the aggravation.