How did people make metal things using moulds? How were they able to melt metal and get it into a mould? Also how did they manage to heat furnaces hot enough to melt metal?
I'll boil down this question down mostly to, "how did they get a fire hot enough to melt metal?" Which is, I think, what you're asking? The answer is charcoal, which burns at a much more intense heat than regular wood, in fact just intense and hot enough to approach the melting point of iron. Making charcoal, or charcoal burning, was actually a job in medieval Europe. Different areas had different ways of doing it, but basically you get a lot of wood together, restrict access to oxygen a bit (often through a soil covering), and then burn it for several hours until it reduces down to charcoal.
The forges were then designed to help make the fire hotter by controlling the burn in an enclosed space and controlling the oxygen getting in to the fire (this is what bellows are for).
You seem to be aware that molds were used to do small work like jewelry. The specific type of casting that would usually be used, though, is called lost-wax casting. The original version of this involved making a wax version of the object, creating a mold by putting plaster or something else around it, and then melting the wax out, either directly with the molten metal or by sticking the mold into heat. That process is still done for small pieces like jewelry. A more complex version was developed in the 16th century which is used for larger pieces like bronze statues. Here's a video from the Getty Museum which explains the latter process very well.