As a planet's core's heat is mostly a result of nuclear decay. Would (leaving the question of how to drill to such a depth aside) adding nuclear waste to the core of a planet, such as Mars, melt the outer layers that have become dormant or would it have no effect? These outer layers are paramount to the magnetic field and keeping an atmosphere (ignoring the obvious problem in the case of Mars that its gravity is too weak).
This is an example of a scale error. Since spoons are used to transfer liquids between containers, can you use a teaspoon to lower the ocean sealevel?
And are you assumptions right? mostly due to decay within the core (isn't uranium in the mantle and not in the core since it doesn't mix with iron? What about residual heat and heat of crystallization as the outer core solidifies?)
Outer layers provide magnetic field?
If you melt the outer part of the core, won't it rapidly lose heat to the solid part, which is a big metal thing which conducts heat easily?