Yes, as that's what the rule says you can do. If you are having trouble visualizing it, "steam" might help.
You can freely have e.g. flaming and frost enchantments on the same sword - there's no "they cancel each other out" rules anywhere. If you allow it, you figure out how to justify/skin it, but combinations of "opposed" energies are completely rules-legit.
Note also that you're slightly confusing classically opposed elements like fire/water and earth/air with the D&D energies - acid, cold, fire, etc. Fire is both an element and an energy type, while water is only a descriptor and cold is a damage type and a descriptor. Water is in the spell descriptors but not the damage type; it's a spell with fire and water descriptors but a damage type of fire.
No, with the latest errata and clarifications from paizo available here. In fact, this specific interaction with Conduct Energy is called out in the section for the Lost Omens Ancestry Guide that the ability comes from:
What actions qualify for the requirements of the resonant weapon
trait's Conduct Energy action?
You can only use Conduct Energy with actions that have one of the
required energy traits. Using an action other than a spell that causes
damage with the listed trait does not necessarily qualify unless the
action also has the trait.
For example, if you used the ifrit's Scorching Disarm action, you
could channel fire energy into your weapon via Conduct Energy, as
Scorching Disarm itself has the fire trait.
However, if you made a Strike with a flaming weapon, the Strike action
does not have the fire trait, so you couldn't use Conduct Energy.
So Strikes made with rune-etched weapons don't inherit the associated elemental trait. Such Strikes are still considered magical, by this line under the Damage Types section:
Furthermore, most incorporeal creatures have additional, though lower,
resistance to magical physical damage (such as damage dealt from a
mace with the magic trait) and most other damage types.
Interestingly, the original printing of the Core Rulebook had a contrary section to this on page 451, Damage Types and Traits, quoted below. The section was removed silently in the second printing.
Damage Types and Traits
When an attack deals a type of damage, the attack action gains that trait. For example, the Strikes and attack actions you use wielding a sword when its flaming rune is active gain the fire trait, since the rune gives the weapon the ability to deal fire damage.
Finally, you wouldn't deal quite that much damage in any case. As @WeirdFrog mentioned, conducting weapons only deal an additional 1d8, not xd8 as you've suggested.
Best Answer
It Depends Upon the Options
Duplicate Effects
The rule points out cases where "you're affected by the same thing multiple times", even giving a spell example in mage armor. The effect of mage armor is an item bonus to AC and potentially saving throws, and casting it again would give exactly the same effect to the character.
It does note that casting a spell again at a higher level might give an enhanced effect, so casting a second more powerful mage armor would give a larger bonus.
Resist Energy
The effect of resist energy is that the target and their gear gain resistance to the chosen damage type. For the same reason as mage armor, resist energy (fire) wouldn't stack with another casting of resist energy (fire) and just the highest level or newest casting would apply.
However, is resist energy (cold) the "same thing" as resist energy (fire)? It grants the target substantially different effects between castings, so I would say this isn't a duplicate effect on the target.
An alternate interpretation could be that the "same thing" is the spell being used, but based on the title of the section that rule comes from, duplicate effects, this seems to be a better way to interpret the interaction.
The final line under duplicate effects about casting a spell again giving no advantage would be explaining the generalized case, for the vast majority spells that always grant the same effect to the user. This is in line with the overarching idea of this answer, that these rules cover duplicate effects instead of duplicate spells.
With Other Sources of Energy Resistance
Another case to consider, what if the target of a resist energy (fire) spell was also wearing a ring of fire resistance? If that target was exposed to fire damage, which of the fire resistance effects would block the damage?
I'd say this is a case where the creature does have a duplicate effect, fire resistance, and that the highest level (depending on heightening) or most recent effect (the continuously applied ring) would likely apply.
Note also that the resist energy protects the target's equipment while the ring does not. This means that even if the ring was stronger or more recently applied, the spell would be protecting the targets gear. Only the duplicated part of the effect would be ignored in either case.
Additionally, a heightened resist energy (fire) that gave fire resistance 10 or 15 would be the "same thing" as fire resistance 5 given by some other source, following the same reasoning as with mage armor. And by the final line under duplicate effects about getting better effects, the higher resistance would apply.
Other Spells/Effects
Spells can do all kinds of things, so this really needs to be evaluated on a case-by-case basis. If the effect of one casting would be the same as any effect currently on the character, then it should be resolved by following the rules for duplicate effects.