Increased fire damage and IFD with Wheapons?

So guys here's my build: Shield + 1 handed Axe with Fire DMG

My auto attack that's for mass of mobs, and actually for bossess too, is Infernal Blow which has been stacked up with supported fire DMG gems:
And also I use the Molten Shield spell:

My question is about these passives "Fire damage" and "Lava lash".
Infernal blow converts 50% of phys to fire dmg, do the passives increase these 50% fire dmg?
= if I hit with 100 dmg, with all phys dmg passives, and 50% is converted to fire those 50 dmg to be boosted with the 6% per passive fire dmg and the 30% more weapon dmg = 50 dmg + 50 + 60% ~ 80 dmg fire and 50 dmg phys the other not converted dmg?

Also I guess Lava lash doesn't boost Molten Shell but the "Fire damage" passives do?

Yes and No. If you hit with 100 base damage (without passives) you'll get 50*1.30 fire damage (with lava leash). The physical passives are still calculated for the 100 damage, but the fire passives won't stack on them because of the conversion- the reason for this is that they don't want the fire passives to become multiplicative only because you are converting damage - if they are additive, they are always additive.