question: does fire immunity reduce damage from dragon's breath, fire elemental, etc.?

Exactly. There's some percentage involved... it all depends on what gave you the immunity. An artifact or a potion (potions seem to give 25%). It also helps against Ifrits and their fire aura. :)

Well, I haven't played the fourth game much, so I don't even really know the unique abilities of each element (if they even exist), but earth will have more health, and I just really like the fire element's appearance, especially with its "paws."

A lot also depends on personal preference... and how well you've played with them. Maybe the earth element is also good; I just prefer water.
All the elements have Elementals (i.e., they are immune to a number of different spells, like Poison and others, which usually cannot be used against Undead), but there are also UNIQUE abilities, and here they are:
1. Water (HP 38, damage 6-9) - elemental + mage (i.e., casts spells like Quicksand, Ice Bolt, Weakness, and Fatigue) + cold resistance (immunity and thus takes less damage from cold attacks) + cold attack (i.e., even in melee). I also want to note that there are no limits to Ice Bolts, and it always fires, even in melee.
2. Air (HP 40, damage 6-10) - elemental + flight + ethereal (i.e., 100% protection in ranged and melee combat)
3. Earth (HP 50, damage 9-14) - elemental + magic resistance and less damage from direct damage spells (like Chaos)
4. Fire (HP 50, 7-10) - elemental + ranged attacker (but in melee, they only deal half the normal ranged damage)

So, we draw conclusions. But the water element definitely has more bonuses!