How does the number of electrons and protons determine the melting point and hardness of a solid? How does the number of electrons, neutrons and protons determine the melting point and hardness of a solid/metal?
And is it possible to create custom elements which is very strong and have very high melting point through fusions and fissions or by getting inspired by the universe that how the universe created different elements out of only hydrogen and helium?
 A: An atomic species defined by its number of protons (usually denoted $Z$) and its number of neutrons (usually denoted $N$) is called a nuclide. For atomic species the number of electrons is the same as the number of protons (i.e. $Z$). You are right to assume that the nuclide of a single nuclide solid will typically determine its melting point and hardness (although the number of neutrons plays a marginal role and some species exhibit allotropy). There is, however, no simple relationship.
From quantum mechanics we can derive a number of physical and chemical properties of a nuclide (mostly dependent on $Z$), but to answer the question of melting point we also need solid-state physics and thermodynamics/statistical mechanics. Even though we may have physical theories that explain how $Z$ relate to the melting point, we may not be able to make accurate, purely theoretical predictions of the melting points based on $Z$ alone. Predicting crystalline structure, for example, is certainly a non-trivial problem.
The prospect of creating synthetic nuclides with properties superior to those of the natural occurring ones has allured scientist for a long time. One problem is that synthetic nuclides tend to be unstable, which is typically the reason that they are not naturally occurring. There are, however, theories that predict an island of stability for certain super-heavy nuclides. Synthesizing these, however, have proved to be very difficult, so the existence of this island remains an open question.
A: Atoms and molecules that have high boiling points and melting points have strong intermolecular bonds that resist   form change. Therefore, to make a material win these properties, in general your you want long chained molecules.
A: It's not even that simple,  as different crystal structures of a given molecule can have different melting points, e.g. Ice-V .
I don't remember enough solid-state physics to state whether any elements form different crystal structures with different melting points, but certainly, for example, the hardness of carbon depends on whether it's diamond or coalblack.
