Do elementary particles have half life? Can we theoretically calculate half of a particle which is in complete isolation?
Some elementary particles, such as the electron, are stable; others, like its more massive sibling the muon, are unstable and decay into other particles. A muon decays through the weak interaction into an electron, a muon neutrino, and a electron antineutrino, all of which are elementary. The muon’s half life is 1.56 microseconds, and this can be calculated from Fermi’s Golden Rule.
The free neutron decays, but physicists do not consider it an elementary particle because it is a composite bound state of other particles.
According to the Standard Model, the only elementary particles are the three charged leptons $(e, \mu, \tau)$; their corresponding neutrinos $(\nu_e, \nu_\mu, \nu_\tau)$; six kinds of quarks $(u, d, s, c, t, b)$; the gluon $(g)$; the photon $(\gamma)$; the two weak bosons $(W, Z)$; the Higgs boson $(H)$; and their antiparticles. (Some particles are their own antiparticle.)
Can we theoretically calculate half of a particle which is in complete isolation?
Yes, and in fact that's generally the easier case. Neutrons, for instance, decay over about 880 seconds - but only in isolation, not within a nucleus (although the reason gets complex).
In a general fashion, you can see a correspondence between the mass of the particle and its lifetime. So, for instance, a W masses 80400 MeV and lasts a very short time around 10^-25 seconds, while a neutral pion masses 135 and lasts 10^-17. However this is not a solid rule; the proton masses 938 and lasts, from what we can tell, forever.