Nuclear Physics Explanation for Each Taste

This might sound silly. But we always talk about nuclear fusion in stars and I have always wondered why this process happens at all.
Is it inevitable for fusion to happen at the temperature and pressure present in a star?

Suppose there exists an alpha particle in the nucleus. Within a radius of 2 femtometer, the dominating force is the nuclear force but beyond this radius, the Coulomb force becomes the effective dominating force due to it's longer range force. Outside this radius is a daughter nucleus.
So let's suppose the alpha particle moves beyond the effective range of the nuclear force,
the electric potential energy due to the force between the alpha particle and the daughter nucleus is given by as
$U_B=\frac{1}{4\mathrm{\pi <!--\; \pi \; -->}{\mathrm{\epsilon <!--\; \epsilon \; -->}}_0}(\frac{2(Z-<!--\; -\; -->2)e^2}{R}).$
Why is there the term
$2(Z-<!--\; -\; -->2)?$

Why is the alpha, beta or gamma decay of an unstable nucleus unaffected by the chemical situation of an atom, such as the nature of the molecule or solid in which it is bound? The chemical situation of the atom can, however, have an effect on the half life in electron capture. Why is this so?

Electric potential energy after nuclear fission
We have a uranium-236 nucleus that fissions into two equal fragments, and I'm supposed to find the electrical potential energy just as the two fragments split apart. No other information is provided.
I am very confused about this problem for two reasons. First, U-236 is electrically neutral, with exactly 92 protons and 92 electrons. After it splits into two equal fragments, why would there be a charge on the resulting pieces? Secondly, electric potential energy of two point charges is inversely proportional to the distance r between the particles. But since the question asks for the potential energy immediately after fission, r=0 and potential energy goes to infinity.
I'm appreciate any guidance!

What is the half-life of Uranium-238?

Binding Energy and Stability in Nuclear fission
I've read that particles in nuclear fission disintegrates into two particles with higher binding energy, and in this process energy is released. Now I am just trying to understand this by common sense, but I am not able to. Because the particle with lower binding energy makes particles of total net higher binding energy, meaning that it takes more energy for the particles with higher binding energy to be formed from the particle with lower binding energy. Hence, shouldn't energy actually be absorbed in this process? Could someone explain where is my reasoning wrong?

Radioactive element X has a half-life of 30 days. A rock sample contains 4 grams element X when it forms. How many half-lives will have elapsed in 90 days? How much of the original amount of X will be unchanged after 90 days?

In stars such as the Sun, what prevents the whole thing exploding at once? Why is the nuclear fusion happening slowly? I can only assume that something about the fusion is fighting the gravity and slowing the fusion down and when that process is done gravity starts the fusion process again.

We already have hydrogen bomb, why controllable nuclear fusion so difficult? And why controllable necessary? If we can detonate a tiny hydrogen bomb， we can collect the energy, like laser nuclear fusion do? Why didn't see any research of collider of coil gun? Beside LNF and Tokamak, using collide, we can let reaction happen in a space far from fragile device.

What is half life decay?

What is nuclear waste half life?

Why is a nuclear fusion reactor not currently possible?
Nuclear fission reactors are fairly common, but what technological/physical limitations are currently impeding developing the nuclear fusion reactor? The H-bomb is capable of creating nuclear fusion on earth, so the process of creating nuclear fusion is already understood to some extent, although you are detonating a fission bomb to start the fusion process.
Having a cycle between a fusion and a fission reactor would solve some serious energy problems.

The SNF accounts for 99.9% of the mass of an atom.
So if 4 hydrogen atoms become 1 helium atom during nuclear fusion does that change the proportion of SNF as we have 4 SNFs becoming 1 SNF and 12 particles becoming 6 particles. Is it now 99.8% or something?

I'm trying to write a paper arguing for why we should spend more money on nuclear fusion research. I keep reading that "nuclear fusion produces no long lived radioactive waste", but when I looked up why this is the only good source I could find was Quora, clearly not something I can really cite. So, I was hoping someone here could explain it to me, and hopefully also leave their sources so I could use them as well.

I have studied about nuclear reactors and also know their functionality.But some how i couldn't get answers for some my questions.
1) During fission reaction enormous amount of heat is produced and this heat is in the form of flames?
2)If so does the whole reactor core is burnt?and how come water can be in contact with the burning core?
3)Once a fission process is finished will reactor be ready for next usage or it will left for years for less radioactive?
4) Whether the chain reaction is started by introducing neutrons or done automatically by spontaneous emission of fuel rods?
5)If it is due to neutron introduction then how these neutrons attack the pellets containing uranium correctly and how many tries are required?
I have searched for many sources online but couldn't get a clear image.Hope get now.

How does the half-life of a nuclide relate to the stability of the nuclide?

What radioactive isotope has a half life of 28million years?

What is the isotope composition of hydrogen atoms in the sun? Are the ratios of protium:deuterium:tritium similar to those we find on earth?
What does the nuclear fusion of hydrogen atoms in the sun look like? Can protiums participate too? Where does, then, the helium atom get a neutron from, as there are no neutrons in protiums?

How does the reversibility of physics interact with nuclear fission
The laws of physics are reversible and quantum information is never destroyed.
Given this, how do I time reverse the $U_{235}$ fission reaction, n which
${}_0^{1}n+{}_{92}^{235}U\to <!--\; \to \; -->{}_{56}^{141}Ba+{}_{36}^{92}Kr+3{}_0^{1}n+\mathrm{\gamma <!--\; \gamma \; -->}+$ 202.5 MeV (in kinetic energy plus gamma ray energy).
That is, would reversibility require that if we bring together the $Ba$, $Kr$, $3ns$, and the $\mathrm{\gamma <!--\; \gamma \; -->}$ all at the same instant, a $U$-$235$ and a neutron might just pop out with a certain probability?

How can I calculate nuclear half life?