If you have n free protons and m free neutrons , the sum of the masses of the free nucleons is always larger than the same n+m bound in a nucleus.
The difference is what generates this plot:
It shows against n+m how bound is each nucleon(proton or neutron) within the nucleus. How much energy would be needed to set a nucleon free.
Fission happens to nuclei after Fe to the right in the plot, fusion to light nuclei on the left of F
In fission, does the nucleus divide because of the collision between the neutron and the heavy nucleus, or because the nucleus would become unstable after the mass number has increased.
How stable a nucleus is , is a solution of the quantum mechanical problem of having so many nucleons bound in a "box", there are stable and unstable levels, as the other answer states, that depend on the number of protons and neutrons and how the levels are filled. There might be spontaneous decay to lighter nuclei , the sum of which will release energy. In general adding a proton or a neutron may change a nucleus to a less bound one that has a high probability of decay, or may immediately break up as with uranium nuclei ( see the other answer).
why does adding a new neutron or more to any nucleus without changing the number of protons, make the nucleus unstable?
a)The neutron when free decays within 13 minutes. When bound in the nucleus in a stable energy level it will not decay, and it helps overcome the electrostatic repulsion of protons between them. But if there are too many neutrons, they are not in a stable energy, but there is a probability that the weak decay will generate a beta decay
b)The solution of the collective potential after adding a neutron may push the nucleus into an unstable energy level, as happens with Uranium.
My book mentions that when alpha decay happens ,a decrease in mass turns into kinetic energy gained by the products.
For any decay, since energy is a conserved quantity, adding the new masses and finding a deficit, means that kinetic energy must be taken by the decay products.
the process of losing mass for energy and vice versa in fission and fusions, shouldn't the mass for the neutrons shot out of the mass increase back and that's it? where would energy come from?
The neutron always has the same mass when free.
In fusion, there will always be at least three particles involved because momentum has to be conserved also. See this article for detailed examples.
The energy comes from the difference in the binding energy between the initial and final nucleons. Helium has high binding energy, hydrogen zero. To bind a proton and an neutron and get an deuterium, releases energy (though it is more complicated than just two particles, look at the link)
In fission one goes towards higher on the left binding energy, so energy is released in the decay products.
Maybe this classical example will help about binding energy: There is a lake up in the mountain. The water is at an energy level. Making a dam and putting turbines the water falls to a lower energy level giving up the potential energy to the flow and the turbines.