What metal might work?
Most metals will not melt in "typical" fires, with tin (thanks, Alexander!) being an exception; tin melts at almost exactly the auto-ignition temperature of books.
Brass, bronze, copper, silver and gold all melt around 1,000°C (give or take 50-150°). Some alloys of iron melt around there, while others need higher temperatures. (This chart may interest you.) Lead also has a low melting point (though not as low as tin), but is of course nasty stuff. Metals with near-room-temperature melting points are probably not useful for your purposes, and at least mercury is also really nasty stuff.
Keep in mind, however, that not understanding that metals melt if you get them sufficiently hot implies a really bad grasp of what we'd consider "basic" science. After all, we see phase changes in ice all the time, and they'll almost certainly know about phase change in fats and waxes. A much more likely issue is going to be not being able to make a sufficiently hot fire. However, you should be able to get to around 1,100-1,200°C with just charcoal (in a suitably lined chimney). If they know the basics of a blast furnace, they can probably melt iron, too.
Could you make a key by pouring metal into a clay mold?
Well... that depends on what you mean by "clay", which can mean a lot of things. The sorts you might use for ceramics can probably take the heat, though. Actually, most minerals tend to have higher melting points than metals, and "fire clay" can be as high as ~1,700°C. For that matter, even today many metal casting molds are still made from clay/sand/rock.
The important thing is firing the mold first. If your character doesn't [know to] do that, the mold will explode when the water mixed with the clay flash-boils.
How could the character handle it without specialist gear?
Short answer: not possible.
More useful answer: the "specialist gear" necessary is not actually that complicated. You only need two or three things.
First, you need a crucible. This is just a bowl made out of something with a higher melting point. If you're using tin, this could even be iron, but it's most traditional to use rock. If you're sticking to something with a melting point around 1,000°C, granite will probably do in a pinch. Fired clay might work (I want to say it will, but might only survive a few uses).
Second, you probably want need tongs. You aren't going to be touching that crucible with your bare hands. Metal tongs are traditional, but might be hard to find in your situation. This may be your biggest sticking point. A dense, hard wood with a high ignition temperature might work (especially for tin), if you don't mind that you might have to try several times.
Third, you probably want something to protect your hands/arms from spills. Good, thick leather gloves may be sufficient.
If you're sufficiently clever (to create a setup that minimizes the time you need to be in contact with the crucible) and/or don't mind possibly getting very serious burns, you might be able to get away with only one of the latter two items.
FWIW, I recommend watching some videos on backyard metal casting; this will give you a better idea of what's involved.