  We prove the well-posedness of solutions to McKean-Vlasov stochastic
differential equations driven by L\'evy noise under mild assumptions where, in
particular, the L\'evy measure is not required to be finite. The drift,
diffusion and jump coefficients are allowed to be random, can grow
super-linearly in the state variable, and all may depend on the marginal law of
the solution process. We provide a propagation of chaos result under more
relaxed conditions than those existing in the literature, and consistent with
our well-posedness result.
  We propose a tamed Euler scheme for the associated interacting particle
system and prove that the rate of its strong convergence is arbitrarily close
to $1/2$. As a by-product, we also obtain the corresponding results on
well-posedness, propagation of chaos and strong convergence of the tamed Euler
scheme for McKean-Vlasov stochastic delay differential equations (SDDE) and
McKean-Vlasov stochastic differential equations with Markovian switching
(SDEwMS), both driven by L\'evy noise. Furthermore, our results on tamed Euler
schemes are new even for ordinary SDEs driven by L\'evy noise and with
super-linearly growing coefficients.
