Which is the only metal that is magnetic at room temperature among these?

The question's premise is too tight, and that is the interesting part. Iron is the famous one, but cobalt and nickel are also ferromagnetic at room temperature, and gadolinium is on the edge of it - it becomes magnetic slightly below normal room temperature, at about 20 degrees Celsius.

Ferromagnetism happens when the magnetic moments of electrons in neighbouring atoms line up spontaneously and stay lined up, which requires an unusual arrangement of unpaired electrons in a particular spacing. Heat destroys it: above a threshold called the Curie point the alignment breaks down and the material becomes merely paramagnetic. Iron's is 770 degrees, which is why a magnet in a fire stops working before it melts.

The strongest magnets are alloys rather than pure metals. Neodymium magnets - neodymium, iron and boron - are strong enough that fist-sized ones are genuinely dangerous, capable of taking a finger off, and they are in every hard drive, headphone and electric motor. Which is why the rare earth elements, which are not actually rare but are concentrated in a few places and unpleasant to refine, became a strategic concern.