Question

Will our earth's core stop spinning when the sun dies?

Answer 1

⬇ ANSWER ⬇

Well no.

When the sun "dies," as you say, it will have first ballooned up into a red giant and will most likely envelope the first 3 planets which of course includes the earth. The earth will simply cease to exist.

The earth's core, primarily made up of nickel and iron, is molten from the extreme external pressures upon it plus some heavy metals like uranium which add heat through radiation.

HOPE IT HELPS ☺☺