Are all Inconsequentia quests solvable

The Bad Weapon and Hands Full (the debuff for wielding two weapons without the Dual Weilding skill) do not affect any of your statistics, but instead cause a direct percentage loss to your damage output when using melee weapons.

Bad Weapon reduces damage by 28%.
Hands Full reduces damage by 36%.

I'm not sure how these stack (whether it's a straight 64% drop, or compounded ~54% drop).

_{See the Bad Weapon page on the wiki if you want confirmation.}

Ingots have limited uses outside of forging. They can be:

• Ground with an Elven Grinder, to make ingredients for potions,
• Sold to Brax,
• Transformed into lutefisk with the Hodaric cube.

If you chose to transform then, you should rather make something like bolt from them, in order to obtain more lutefisk from one ingot.

Edit: If you want to sell them, you should before try to craft them into something more valuable, depending on the ingot type:

• Plastic into plastic ring,
• Copper and tin should be made into bronze then a dagger or gladius, if you don't have enough tin, make a cooper ring,
• With iron, try to make steel then a steel cuirass or even a full plate armor if you have enough,
• With aluminum, also try to make a cuirass,
• Zinc, brass, silver, gold, electrum and platinum are good sold directly.

There may be better deal with cross-metal crafting, but this is what I found for direct metal crafting.