Yeah the slag is kind of brittle so the smith could simply knock it off. Thus by repeating this process of heating and hammering they could get rid of all lot of the slag and be left with more pure iron.

Of course this is a lot of work, which is why they would eventually use water powered trip hammers to hammer larger chunks of iron.

I don't think I had that clear idea of wrough iron either, but it seems what was closest to steel of what they had back then. The boundaries between different iron-carbon alloys are kind of fuzzy though.

I believe when then worked with wrought iron they would often end up with parts of its being more like steel. The hammering left some parts with a more optimal mix than others. Like a steel sword would not necessarily be steel all over as far as I understand. They could e.g. have hammered the edge into steel while the rest was closer to wrought iron in properties.