Yes i have a arcane archer he will be happy

What would the official ruling be on using this for sling ammunition?

Arcane Archers should be able to learn this spell naturally. Of course maybe have it so that they can only use it once per long rest or something. 

Average 3.5 damage per hit, for a third level spell and it uses your concentration?  Help me understand why this is even half as good as conjure animals, fireball, haste, hypnotic pattern?

What exactly is the point of this spell? Hunter's mark does the same damage, isn't limited to 12 shots, costs a 1st level slot and only takes a bonus action to cast. Also by the time you get 3rd level spells, you're most likely wielding a magical weapon so you'll go through resistances, while fire is commonly resisted. 

If you're not a Ranger and you wanna buff your archer, this doesn't even compare to Haste.

Yes this totally overshadowed by hunters mark, the only benefit here is that you can give this buff to someone else in the party ¯\_(ツ)_/¯

if you have a hunter in the party, he casts hunter mark. the sorc wizard or druid then casts this on him too so now hes doing 2d6 extra damage?   1d6 fire 1d6 from the hunters mark. i can see this for very long range fights to kill them off before they reach the party. but then your using a level 3 spell and 1st to get this.  really reasource heavy for 2d6

hunters mark has a 90ft range so even that niche scenario is too good.

My suggestion is to just make this not have concentration.

Would the Alchemist's Alchemical Savant be able to utilize this? I understand why, but why not?

Tbh, this needs to be an 8 hour duration and be non concentration. 1d6 of the most commonly resisted element isn't worth a 3rd level slot. 

that would make it a bit to powerfull, imho all it needs its to be a 1d8 instead of 1d6

Can this be used on firearms?

Tip for DMs, make this a first level spell.

Edit: ... Nope.

Quote from GuitarBerserker >>

Would the Alchemist's Alchemical Savant be able to utilize this? I understand why, but why not?

 Nope.  There is no damage roll when this is cast, there are no damage rolls from the spell itself. Its target is the enchanting of the arrows.  So it doesn't count for that ability.   its kind of weird but due to the wording on both spell/ability the fire damage roll on this isn't the spell's damage roll, its the arrow's.  Unlike say flaming sphere (which you get once and only once).

If you have a Character "Fighter" or  Ranger that uses a Bow for a main weapon with Mage Initiate feat, just imbue your arrows with one of the cantrips that you are allowed to choose from.

Craft Magic item at Character level 3:  DMG PG 128-129 and Magic Power by Rarity:  DMG pg 284-285 for reference.

20 arrows = 1gp

Common item 100GP = 8hrs a day 25gp = 4 days of work or 16Hrs a day 50GP = 2 days of work.

Spell is Cantrip and there is no spell slot needed:  Poison  Spray 1D12,__ Produce Flame 1D8__ Sacred Flame 1D8 at character level 3.

Give command word for Activation, No Casting time, No Concentration and Damage is delivered on impact. + with Hunters Mark there is the extra damage of 1D6. No need to waste a spell slot.

for a ranger, hunter's mark is a much better option

Surely the point is the ability to cause fire damage, as opposed to piercing? Some creatures are resistant to piercing damage but vulnerable to fire...?

but i believe that the piercing damage from hunters mark counts as magical, and i don't think any creatures have resistance to magical piercing damage.