What’s the effect of dual-casting soul trap

How much magika will be consumed/needed to cast the spell (just the double of a normal one?)

It seems that dual casting cost a LOT more than just double the normal cost.

Single cast fireball - 42 magika
Dual cast fireball - 117 magika

Single cast chain lightning - 49 magika
Dual cast chain lightning - 137 magika

Single cast fire rune - 74 magika
Dual cast fire rune - 206 magika

Single cast conjure familiar - 44 magika
Dual cast conjure familiar - 122 magika

In all, looks like you will be using roughly 2.8x the magika cost of the single cast spell.

How is the spell affected? (How much damage does it deal? Or how much does its heal?)

For conjuration spells, dual casting doubles the conjuration life span of the spell.

For destruction spells, here are some damage values:

I used Cicero as my dummy target since its always fun beating up a clown.

He started out at 375 health (you can see a NPC's health by selecting them via the console and typing in getav health). You can also use this to see every other skill/stat of theirs. I avoided fire spells since they can burn and throw off some numbers with its burning damage.

Single ice spike: 25 damage (exactly matches the expected value I see by selecting the spell)
Dual ice spike: 55 damage

Single lightning bolt: 25 damage
Dual lightning bolt: 58.23 damage

Overall, it looks like damage is increased by roughly 220%

Keep in mind that impact will knockback the target if you get the perk.

For any other duration spells, the duration is doubled as well but the effects remain the same (stoneflesh still boosts armor rating by 60).

Dual casting the ward spells doubles the armor bonus.

How are runes affected by dual casting? ("Trap"-Runes on the ground)

1 handed Frost rune damage: 50 (matches expected value)
1 handed Frost rune attempt #2 35 damage
1 handed Frost rune attempt #3 22 damage (lol)

2 handed Frost rune damage: 64
2 handed frost rune attempt #2 55
2 handed frost rune attempt #3 75

The damage is not quite doubled, but the damage itself from the rune varies greatly due to the location of the rune and how close the target is to the center. Its entirely possible the rune damage is also doubled, but its very rarely that you actually hit for the max amount.

What does this mean?

It means, you can take out your completely empty Sword of Flaming Flames, kill a bear with it, and now it's got 5% of the bear's soul for the next fight. (note: works for partially filled magic items too)

Does this require you to have an unused soul gem in inventory for it to work

Nope.

and how does it interact with a soul trap weapon?

1. The soul trap weapon casts soul trap on the creature.
2. The creature dies.
3. 5% of the creature's soul is stored to the weapon.
4. 100% of the creature's soul is stored to an empty gem.

Yes, that is 105% of the soul, which is awesome.