Alright as for this Fire in relation to advanced elements, I suppose it would be best to show how Fire works in combination to make advanced elements, then how it works with advanced elements (without Fire), and then Fire in opposition to other elements.
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Fire+Earth=Lava: Perhaps the most commonly recognized combination with fire. The super heated properties of the fire added with the earth's solidified nature creates a somewhat liquified and molten earth which melts most substances upon contact and the extreme heats can even cause substances to catch fire. There is the variation of the style which is Rubber, used by Dodai, however I'm not sure on every extent as to how this occurs.
Fire+Earth=Steel: This element lacks in several areas in it's development as it was only demonstrated in a movie and showed one technique which was very similar to the Earth Release technique used by Kakuzu. However, on that note the properties of steel, the use of fire and earth to create the refined metal element is assumed to be how the technique came to be. An advanced version of Earth release. To my knowledge the usages can span as far as creating metalic, steel items in a similar fasion to earth techniques (for custom sake). THe only canon technique shows the incorperation of manipulating the chakra on the body. However I theorize that their could be a liquid property. Before steel cools and hardens into the metal it becomes it's an extremely hot liquified state. The Fire property within the style we can assume can get so super heated to get to the tempetures of the steel's melting point and create that liquified form of the metal. Since there is very little useage on the base and the scope of the technique is very limited from the perspectives we're given.
Wind+Earth+Fire=Dust: Not too sure on this combination tbh.
Fire+Lightning=Dark: As Dark Release is not a traditional element, there is really no way of telling what the elements are that make it up or if there would actually be any. Based on the explanation in the thread about Dark Release, since Lightning and Fire adhere to the properties of Yang, and Dark is generally associated with the Yang nature, the consensus was to add the Fire+Lightning combo as the duel combination.
Fire+Wind=Scortch: I'm not an expert here either, though from my interpritation of the relationship, The Fire release nature adheres to the ability for the users of this element to burn up/evaporate the water in your opponent's body. I presume the nature of wind is used to circulate the chakra in the air and in your opponent's body.
Still adding...
The Earth + Fire = Steel is more about maneuverability than anything. The earth gathers the minerals and the fire fuses them together. Whether the steel comes out in liquid form or in solid form, the fire plays a part in it's genesis, not just it's state.
Earth + Wind = Scorch is quite simple. Scorch is the element of drought. See it as a very dry and hot current of wind. It has suction, flow and intangibility, but also dryness and heat.
I concur with your definition of Dark. I guess I'd say Fire is about consuming substances feeding on them. Lightning would be the counterpart, as it is also an energy. These are the only energy based elements, and it's probably why they were made into Dark, in addition to the Yang stuff xD.
I've looked up the relation of Lava and Rubber. There is a process of Vulcanization where you heat up the natural rubber polymers to fuse them with sulfur and other compounds normally found in lavas creating a more resistant and elastic rubber, with greater mechanical power. The problem is that rubber itself is an organic compound that comes from trees. I guess here it's recreated with Earth Chakra and then vulcanized by Fire chakra. Not unheard of in the creation of CE. But it's mostly about Vulcanized Rubber.
Same with Cement/Quicklime Congealing, it's about taking a product, calcium carbonate and uses heat to turn it into calcium oxide. This requires the presence of air through. It's a bit sketchy to recreate this with Lava, as no product other than the Heat is found at a normal lava. Lava here has taken a more global definition. In fact, Youton doesn't really mean Lava, but rather molten release, or fusing release, which explains all the variations.
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. (Which would probably mean that one could try passing Steel as Lava release ... hint hint)
Wind+Earth+Fire=Dust, I'm not sure either. I'd say it takes the consumption part of Fire and the density/weight manipulation of Earth, and the lightweight, intangibility of Wind to create a light/intangible element that's so dense that it consumes every matter. Lol. Yeah.
I'll look it up xD