I'm going to answer your questions because I don't want to leave questions unanswered.
However, please note that this is an old version of the rules using an outdated map, so my answers don't apply to the final rules and published map.
Map and rules have evolved a lot since then.
- Can I build a factory or an iron mine in an empty space that does not have the corresponding icon?
Yes. However, when there's a factory or an iron works icon, it is mandatory to build that type of industry.
- Can I buy coal from the foreing market to build in a space if there is coal in the map but is not accessible?
Yes, but only if you are connected to the foreign market.