Is that OK to have the same Prior and Proposal Distribution in MH? Is this ok to choose the same proposal distribution as the prior in Metropolis algorithm?
Perhaps it's a simple question and to me, it's totally fine but as I always see people choose different distributions, I'm curious to see what others think.
Thanks very much in advance,
 A: I get what you're asking (and if I'm right: yes, it is ok), but I think the question is ill-formed.
In MCMC you use a Markov chain to wander over some state space, visiting points of the space with probability proportional to some target function.  The chain wanders from point to point based on some proposal distribution.
The target function needs to be proportional to a probability density, but that's it.  It's not necessarily connected to a choice of prior or likelihood in a Bayesian model.  We fruitfully use MCMC to approximate integrals over posterior distributions in Bayesian statistics, but you could also use e.g. the Metropolis algorithm to approximate the expectation of the distribution with density proportional to the function
$$
f(x, y) = \exp \left\{-(1 - x)^{2} - 100(y - x^{2})^2 \right\}.
$$
Notice I haven't specified a Bayesian model consisting of prior & likelihood; I've just given you some function that is proportional to a probability density.
So: yes, feel free to use the same proposal distribution as your prior, if you're performing MCMC on a posterior.  The two are not meaningfully connected.
A: It was not completely clear whether you meant the same distribution, but centered on the previous value of the chain or independent proposals drawn from the prior. Either of the two are no problem per-se, but are potentially inefficient. 
Ideally, you would have independent draws from the posterior as your proposals, but that is of course in practice infeasible. Compared to that a proposal that is much wider more dispersed (which would often be the case for a prior, whether it is centered on the previous value of the chain or not) typically leads to a very low acceptance rate.
