Nuclear Reaction
Because the structure of their nuclei is unstable: too many or too few neutrons, excess energy causing metastable state, etc. To get more stable they decay, emitting alpha, beta, and/or gamma radiation.
The energy is called nuclear radiation, high energy particles and rays that are emitted by the nuclei of some atoms.
It is not possible for two particles to touch (via the Pauli Exclusion Principle, which states that two fermions are not able to occupy the same quantum state); however they will interact. In the case of atoms, assuming that they are not merely nuclei, the electrons will interact first via the electromagnetic or weak force.
Joining two nuclei to produce an atom of a different element is called fusion.
The nuclei also interact with each other (being charged particles) and therefore have energy levels which can decay to produce photons.
Radioactivity
The process described is radioactive decay.
B- particles are electrons. They are not Helium nuclei.
Nuclear fission
Alpha particles are positively charged helium nuclei. As such, they are repelled by other positively-charged nuclei. In Rutherford's experiment, he used gold foil. Since gold atoms have large, massive nuclei, the alpha particles were easily repelled by the large gold atom nuclei, and they were scattered in different directions.
Radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability. It is also known as a decomposition process.
It is not clear what is meant by 'beta'. Please rephrase it in a new question. It's pretty obvious this question is about radioactivity and the beta particles produced by that. In fact beta particles are not the least penetrating. It is the alpha particles that penetrate least. That's because they interact easily with atomic nuclei. Atomic nuclei are positively charged, like alpha particles, causing strong repulsion.
Because the structure of their nuclei is unstable: too many or too few neutrons, excess energy causing metastable state, etc. To get more stable they decay, emitting alpha, beta, and/or gamma radiation.
radioactive decay or simply decay.
Ozone Particles
The so-called alpha particles ARE helium nuclei.
No. Alpha particles are helium nuclei; such nuclei have a mass, and can therefore NOT travel at the speed of light.