Concerning the second question about coherence, Theorem 3 in M.E.Harris, Some results on coherent rings II, Glasgow Math. J. 8 (1967) 123-126 says:

There exists a non-coherent ring $R$ such that $R_{\mathfrak{p}}$ is coherent for every prime ideal $\mathfrak{p}$ of $R$.

Concerning the second question about coherence, Theorem 3 in M.E.Harris, Some results on coherent rings II, Glasgow Math. J. 8 (1967) 123-126 says:

There exists a non-coherent ring $R$ such that $R_{\mathfrak{p}}$ is coherent for every prime ideal $\mathfrak{p}$ of $R$.

Concerning the second question about catenarity, the answer is obviously yes.