Molten Strike

"I assume the projectiles are a completely separate attack and count as a completely separate attack."
Naturally.

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"It the base dmg multiplier included with the % increased damage or is it calculated before those?"
It's of course a separate multiplier. Pretty pointless otherwise :P
Being a Base Damage modifier, it applies to precisely what it implies: Base Damage. However, being a straight multiplier, it doesn't actually matter when you apply it, as long as it's after flat Damage.

More babbling about Damage, while we're on the subject:
Projectile Attacks do not scale with Increased Melee Damage. You're not getting "120% Increased Damage" from your passives and gear, but something inane like this:
50% Increased Melee Physical Damage (saaay, Strength)
20% Increased Physical Damage with One-handed Melee weapons
30% Increased Physical Damage with Axes
20% Increased Elemental Damage

Which means your Projectiles receive 70% Increased Damage, but the Melee strike enjoys the full 120% ID. In your specific example, you can simply apply the Less Damage multiplier to your Melee hit, but that's not how it'll work in practice. Be wary. :)

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"Anyone know exactly when in the damage calculation damage is converted?"
Of course I do. :P

Conversion occurs before Damage multipliers are added.
Converted Damage benefits from modifiers to the source-type.

Damage Based On, such as Hatred and Added Fire, occurs before Conversion. As such, it is just as strong on Molten Strike as it is on Heavy Strike.


Using the previous list of modifiers, a 100 Physical Damage weapon and 20 flat Fire Damage, Damage work out as follows:

120% Base Damage:
100 * 1.2 = 120 Base Physical Damage
20 * 1.2 = 24 Fire Damage


Melee portion:
120 * 0.6 = 72 Fire Damage (from Phys)
120 - 72 = 48 Physical Damage
24 Fire Damage

48 Physical damage benefits from all modifiers:
48 * (1 + (50/100) + (20/100) + (30/100) + (20/100)) = 105.6 Physical Damage

72 Fire damage (from Phys) benefits from all modifiers too:
72 * 2.2 = 158.4 Fire Damage

24 Fire Damage only benefits from Ele Damage:
24 * (1 + (20/100)) = 28.8 Fire Damage

Sum total:
105 Physical Damage
158.4 + 28.8 = 187.2 -> 187 Fire Damage


Projectile portion:
48 * 1.7 * 0.6 = 48.96
72 * 1.7 * 0.6= 73.44
24 * 1.2 * 0.6= 17.28

48 Phys, 90 Fire