Hey u sound knowledgeable. I got a question. I learned that if you fully melt iron, it will become cast iron and its very brittle and unfit for a sword. Does heating and hammering after casting it help it get out of "cast iron"? I remember it was because of carbon content or something.
I'm not an expert, just picked up stuff from general interest, so you might want to fact check.
Generally, this is what you get from blast furnaces when you process iron ore. It's a type of iron with a high carbon content, and I think that's what's called pig iron, but also cast iron if you use it for that purpose. It's brittle but hard. Brittle is relative, though, since it's still strong for certain applications, as it can take a lot of pressure, but not bending. Normally (in the modern world, at least) you'd refine that by lowering the carbon content to make various steel alloys.
Working iron at an anvil can change the carbon content, but I'm not too familiar with the limits of that.
If it's low carbon content from the start, it can be forged into weapons. It's a bit like melting iron scrap while controlling carbon content, and the result of that can be cast into workable iron or steel pieces. We are also dealing with a magical process and magic iron, so I don't see a problem with that specific part of the process.