Does the alpha particle travel in vacuum for ever and ever or can it undergo some transformation eg two protons get separated or the neutron decays etc.?
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It depends on what theory of everything nature follows. There are some theories that predict that protons decay, so if one of the protons decays the particle will disintegrate as one proton and two neutrons are not a stable system.
In order to have a beta decay of the alpha, the left over system, three protons and one neutron, should be energetically favorable, more bound. This is not true so it is not a transition that can happen within the standard model.
If there exists a new exchange in a new theory which will allow the proton to decay , it means that quarks which carry the baryon number, can disappear, which is not the case within the standard model.
