It’s pretty much the same as the 2014  Dragon’s Breath but with fewer flavor text. I’m not sure how to feel about this, but I guess for a new player it doesn’t dragon and goes straight to the point.

Excuse the wording of this: can you touch yourself?

Yes, you can always touch yourself

The creature doesn't need a mouth anymore. so my black pudding familiar  can use this legally.

I think, you still need the verbal part, as it has the component requirements V, S, M.

Sure to CAST the spell i need V,S,M but to use it it's just a magic action, and it does say the target needs to make that action.

Thanks for clearing this up. Now I understand what you mean.

what a pun

I would say based on the name of the spell and the language that one "exhale[s] a 15-foot cone" that a creature needs a mouth to benefit from this spell and that positing otherwise requires a bad-faith interpretation of the rules.

If only Artificers could cast this.  Alchemist Artificers would have a potion made from spicy peppers that makes you literally breathe fire.  Other Artificers would have a flamethrower.  Imagine being an Artillerist combining this spell with a Tiny Flamethrower Eldritch Cannon to have a more powerful flamethrower (action for Dragons Breath, bonus action for Eldritch Cannon).  Battle Smith Artificers can cast it on their Steel Defender for better action economy (since their Steel Defender naturally spends time on the frontlines).  Any Artificer can cast it through their Homunculus Servant.  

Think of all the possibilities, both mechanically and aesthetically.  

You can exhale out of nothing if you have a spell that doesn't require a mouth. It's magic. The creature doesn't have altered physiology that lets it spit flame, it just spits flame at will. If it does need altered physiology, good news, it's magic. Your ooze opens a little hole in its side and magicly breaths flame out of it compressing itself slightly as it does so. 

Can the creature keep using magic actions on each of its turns to breathe fire (or other damage type)?  The spell doesn't say that it ends when you do so.

Quote from Flying_Dominion >>

Can the creature keep using magic actions on each of its turns to breathe fire (or other damage type)?  The spell doesn't say that it ends when you do so.

Yes. That's why it says "Until the spell ends".

multiclass as an artificer sorcerer 

If cast on a party member or familiar, do they use your (the caster) spell save DC? Also, if you (the caster) have the Elemental Affinity feat, does that transfer over to the party member or familiar using the magic action attack?

Quote from saintwerdna >>

If cast on a party member or familiar, do they use your (the caster) spell save DC? Also, if you (the caster) have the Elemental Affinity feat, does that transfer over to the party member or familiar using the magic action attack?

It would be the caster's save DC. Spells that require saving throws always use the caster's save DC unless the spell explicitly says otherwise, which this one does not.

As for your other question — "Elemental Affinity" is a feature of the Draconic Sorcery subclass. "Elemental Adept" is a feat. They are both relevant to this spell, but they behave slightly differently.

Elemental Affinity says that "when you cast a spell that deals damage of [your chosen] type, you can add your Charisma modifier to one damage roll of the spell". So, it would apply to this spell if you choose the right damage type even if you're casting it on someone else, but it would only apply once, to one damage roll.

Elemental Adept says that "Spells you cast ignore Resistance to damage of the chosen type. In addition, when you roll damage for a spell you cast that deals damage of that type, you can treat any 1 on a damage die as a 2." Both of these benefits would apply when you cast the spell on someone else, and in this case they apply to all damage rolls for it.

A weird quirk here is that because both of these say they only apply to spells you cast, they technically would not apply if you had these features and someone else cast this spell on you.