I was under the impression that iron reacted pretty well with oxygen; is that not the case in the chemistry of a forming earth?

Core is molten for two reasons:

Initial formation of Earth generated a lot of thermal energy, because a lot of stuff smashed together

Continued decay of radioisotopes has contributed additional thermal energy-- without this, the core would have cooled by now

Thermal energy is lost from the core through heat transfer to the mantle, which brings it to the crust by way of convection; this is what ultimately causes plate movement, earthquakes, volcanism, subduction, etc. on Earth. Once the core is cool enough that mantle convection stops, tectonic forces will subside and uplift processes will cease. From that point, weathering and erosion will gradually erase all land above sea level, giving us an ocean planet. I think the Sun will be hot enough to boil our oceans well before that happens, though (solar brightening over geologic time).