Ethereal Knives' interactions

I have two questions about Ethereal Knives.

According to the unofficial wiki: "Physical Damage Spell: Because Ethereal Knives deals physical damage, it can be boosted by supports and skills that are more commonly used to modify attacks, such as the Added Fire Damage support gem and the Hatred aura."

Although, when I try to use Wrath, the DPS on the skill does not increase. I've also read that auras don't apply to the spell because it's a spell, and doesn't use the weapon. Added Cold Damage will increase the DPS, though. So does Wrath and Hatred affect Ethereal Knives or not?

Next question, how does LMP/GMP work with Ethereal Knives?

EK's projectiles won't hit the same target more than once, would LMP/GMP change that? Would only the additional projectiles be able to hit the same target, or would you be able to hit all of them on the same target?

Also, does it change the projectiles to 13 or 30?

Wrath only adds lightning damage to attacks.

Added Fire Damage and Hatred add a percentage of physical damage as elemental damage, making them compatible with Ethereal Knives.

To clear up the confusion:

Auras:
Wrath - adds flat lightning damage to attacks
Anger - adds flat fire damage to attacks
Hatred - adds a percentage of physical damage as cold damage

Added x damage supports:
Lightning - adds flat lightning damage to both attacks and spells
Cold - adds flat cold damage to both attacks and spells
Fire - adds a percentage of physical damage as cold damage

Added Cold and Added Lightning Damage supports add damage to both attacks and spells, and will work with EK.

LMP/GMP are not really worth using with EK since you fire a lot of projectiles already. With LMP/GMP, the projectiles will still only hit a target once. To get multiple hits, use a Fork or Chain support gem.

EK shoots 10 projectiles. LMP would increase this to 12, and GMP would make it 14.