why is the inner core solid despite its extreamly high temperatures?

Answer 1

Extremely high pressure as well. The melting point of iron increases a lot under very very high pressure.

Only the outer core is liquid(when speaking of the 2 cores). The inner core is indeed solid.

Answer 2

The core is NOT solid. It is liquid.The circulating molten conducting core creates circulation electrical currents which in turn create the earth's north and south magnetic poles. If you mean the central part of the inner core, that is very small indeed (about 780 km in size) compared the the rest of the earth's interior. And it is believed that this inner core does not have a uniform density. It has been shown to rotate faster than the earth's crust.