Is this correct: if hot goes to cold- as the first law of thermodynamics says- then the heat from the spark plug is **trying **to find the relative cold surface of the fuel. All the shaping of the chamber and engineering of a misted fuel load injection and so forth is simply to maximise this basic physical need of all object?

No. Yuck. Please don't do that again. It's obscene.

A spark isn't trying to do anything. It just is. The spark is disconnected from later consequence, how well fuel is mixed with oxygen, shape of a cylinder or your need for speed. The spark depends on the potential and the dielectric with various 2nd and 3rd order effects which are mostly corrects to the dielectric.

Beyond that, and this relates to ice melting and freezing, other dynamics are in play than just thermodynamics. Kinetics, convection, diffusion and more. Equilibrium style thermodynamics sets some limits, informs on how the kinetics of various processes changes with T but it's really very complex.

Consider the dual gradients of T and salinity in the water column. Model it as the consequence of what are differential equations involving the rates of diffusion, convection, turbulence, radiation, heat of fusion at the ice/water interface, salt exclusion and on. Simplify it to competing rates. Water pours into a jug at a fixed rate. As the jug fills, increasing the water column, a hole in the bottom of the jug leaks more and more water. Except that can be modeled by a simple differential equation and for freezing/thawing we have so many more variable.

Now it's perfectly reasonable to attempt to consider a single effect, to model a simplified system, or otherwise speculate but please, don't begin with completely bogus physics. Systems don't "want" to do things, or "try" to reach equilibrium or move heat. But I've ranted enough. Bad thermo does that to me.