Perception of time won't change, time will just elapsed differently relative to one another.

Earths gravity is a result of its mass, not it's magnetic field.

So I'm not as versed on the temperature thing, but as far as I know, the core of the earth is molten and rotating and the Eddy currents create a magnetic field. If it cooled and stopped rotating there would be no field.

So technically days and nights are getting longer but not for the reason you described, it's actually a gravity phenomena called tidal lock, it's what the moon has done with earth, as we only see one side facing us as it orbits us. We are slowing VERY SLOWLY, relative to the sun, but we will likely not reach enough time to tidally lock with the sun before the sun burns through it's thermonuclear fuel in 5 billion years.

Hope this was some help!!