[iPromise]

What heat-resistant material is used on the outside of the blast furnance to prevent the heat from the inside melting the entire furnace and its surroundings?

Also, in a blast furnance, air is pumped to the bottom of the furnance right? Doesn't that mean that the molten iron, slag and everything else on the bottom can escape from the bottom towards the hole where the air is pumped?

When you extract the molten iron, where should you put it in -> some people use a steel container? Won't the steel container get extremely hot and melt?

Here is my diagram of how I think a blast furnace should be like, correct me if i'm wrong please:

[curiouscat]

What heat-resistant material is used on the outside of the blast furnance to prevent the heat from the inside melting the entire furnace and its surroundings?

Firebricks / Refractory bricks.

Also, in a blast furnance, air is pumped to the bottom of the furnance right? Doesn't that mean that the molten iron, slag and everything else on the bottom can escape from the bottom towards the hole where the air is pumped?

Large air pressure I suppose... Not sure.

When you extract the molten iron, where should you put it in -> some people use a steel container? Won't the steel container get extremely hot and melt?

Crucibles are typically firebrick lined.

[Arkcon]

Drawn as equal sized squares, like you have, I'd expect no end of problems with leakage.  However, the construction is much more complicated:  http://en.wikipedia.org/wiki/Blast_furnace  The wikipedia page has real pictures, and historical diagrams, and diagrams of contemporary diagrams.  You can see how the charge is held.