After consideration, I'm going to disallow the feat selection on the homebrew race. While I'm not shy regarding homebrew, the Elemental Adept feat already exists with completely different features. The addition of a feat, I think, is probably worth the upper end of the scale that person is using (2-4), as evidenced by it being almost the only notable feature variant humans get. Adding feats to other races also sort of makes Humans less special, and they are by far the most numerous race in Karthun. I also think that all races in 5e should grant some bonus to ability scores, setting them apart in ability from other races in comparison.
While it certainly could work as an invention of the gnomes or Sunwalker dwarves, the overall flavor implies an attempt to bind an elemental spirit to a construct as opposed to a humanoid creature.
I would suggest the following racial traits:
Elementalforged (or Gearbound, depending on the race creating the specific instance)Ability score increase: Your Constitution increases by 2, and your Intelligence increases by 1. (3 pts)
Size: Medium
Speed: 30 feet.
Darkvision (0.5 pts)
Living Construct: Even though you were constructed, you are a living creature. You are immune to disease. You do not need to eat or breathe, but you can ingest food and drink if you wish. Instead of sleeping, you enter an inactive state for 4 hours each day. You do not dream in this state; you are fully aware of your surroundings and notice approaching enemies and other events as normal.(1 pt)
Composite Plating: Your construction incorporates wood, metal, and stone, granting you a +1 bonus to Armor Class. (0.5 pts)
Elemental Source: You are a creature born of the binding of an elemental spirit to an inanimate automaton. Choose one type of elemental from the following options. Your innate magic is determined by the elemental type you choose.
Innate Magic: You know one cantrip, as determined by your elemental source. Once you reach 3rd level, you can cast the spell indicated once per day as a 2nd level spell. (1 pt)
- Element: Cantrip | Spell
- Fire: Control Flames | Burning Hands
- Air: Gust | Levitate
- Earth: Mold Earth | Earth Tremor
- Water: Shape Water | Create or Destroy Water
This results in a 6-point race combining some of the warforged flavor and racial traits, while boosting them with some Magebound flavor and related magic. I tried giving them energy resistance instead of natural armor, but there's nothing relevant for Earth. I'm not too worried, since Artificers (or Magebound, should the Elementalforged pursue a Mage class) would eventually get pretty easy access to energy resistance. If I were posting this race elsewhere, I'd probably give it a +1 to Charisma rather than to Intelligence due to the connection to elementals, and the relation between sorcerer-based casting to Charisma, but I also understand the point is to have a race more suited for your character concept. This worked out well enough.
As for the class, no free action class features. There aren't really any free action abilities anywhere else except where an ability allows you to perform two actions as part of the same action taken. There are actions, bonus actions, and reactions.
As such, the rune arm charging up could result in an attack made as a bonus action or as an action (or possibly a reaction, though that could get annoying if it gets used during other people's turns too often).
I've done a lot of tweaking to
my version of the DDO-inspired Artificer, but my handling of the Rune Arm is mostly unchanged:
Rune Arm
The first arcane invention you craft as an artificer is called a rune arm, a magical device which fits over your forearm. This item acts as a focus for your infusions (see below). At first level, you learn how to channel magical energy through your rune arm to cast a cantrip. You infuse your rune arm with one cantrip, chosen from the following list: Acid Splash, Eldritch Blast, Fire Bolt, Ray of Frost, or Shocking Grasp. Once chosen, the cantrip remains infused in your rune arm until you infuse a different cantrip after finishing a short or long rest. While your rune arm is infused with this cantrip, you may cast it as an action.
Alternately, you may activate your rune arm as a bonus action. Activating your rune arm in this way allows you to make a ranged spell attack with a fixed range of 60 ft., dealing 1d4 damage of a type appropriate to the cantrip infused (acid, force, fire, cold, or lightning). This damage increases by 1d4 when you reach 5th level (2d4), 11th level (3d4) and 17th level (4d4).
You may also cast the Light cantrip through the item, though the effect can only target your rune arm.
The damage for my version of the class hits an average of ~16 like the Sorcerer you mentioned (2d10+2d4) though weapon damage lags behind slightly (1d10+2~5 +2d4, or 12.5~15.5 depending on stat allocation) until the Battle Engineer gets Extra Attack. At 20th level, it hits at about the average you mentioned for par (2d10+10+3d4+4d10, ~50.5; assumes Crossbow Expert feat or a new infusion based on the Endless Fusilade Battle Engineer enhancement). The downside is I created a completely untested spellcasting variant with no way to tell how it would work in practice, and with two very different methodologies for approximating spellcasting power.
My Battle engineer has much more limited infusing but can build up its ability to cast infusions by making weapon attacks. My Arcanotechnician has way more infusing capability, eventually having a spellcasting capability closer to the Sorcerer or Wizard (from a certain point of view). It might just be too convoluted to be worthwhile.
Other than the spellcasting, I tried to fit in as much of the abilities you were looking for as I could, while also trying to impart it with a bit of crafting-focused utility/interaction class features rather than just combat-oriented abilities. All 5e classes are meant to include some passive benefits and other other features to support the interaction and exploration pillars of gameplay, so I needed to do my best to include that as well. --edit-- Also, I am missing features in the last couple levels, but otheriwse...