Static and dynamic behavior of short-range Ising spin glass (SG) ${\mathrm{Cu}}_{0.5}{\mathrm{Co}}_{0.5}{\mathrm{Cl}}_{2}\ensuremath{-}{\mathrm{FeCl}}_{3}$ graphite bi-intercalation compounds has been studied with superconducting quantum interference device dc and ac magnetic susceptibility. The T dependence of the zero-field relaxation time $\ensuremath{\tau}$ above a spin-freezing temperature ${T}_{g}(=3.92\ifmmode\pm\else\textpm\fi{}0.11\mathrm{K})$ is well described by critical slowing down. The absorption ${\ensuremath{\chi}}^{\ensuremath{''}}$ below ${T}_{g}$ decreases with increasing angular frequency $\ensuremath{\omega},$ which is in contrast to the case of 3D Ising spin glass. The dynamic freezing temperature ${T}_{f}(H,\ensuremath{\omega})$ at which ${\mathrm{dM}}_{\mathrm{FC}}(T,H)/dH={\ensuremath{\chi}}^{\ensuremath{'}}(T,H=0,\ensuremath{\omega})$ is determined as a function of frequency (0.01 Hz $<~\ensuremath{\omega}/2\ensuremath{\pi}<~1\mathrm{kHz})$ and magnetic field $(0<~H<~5\mathrm{kOe}).$ The dynamic scaling analysis of the relaxation time $\ensuremath{\tau}(T,H)$ defined as $\ensuremath{\tau}=1/\ensuremath{\omega}$ at ${T=T}_{f}(H,\ensuremath{\omega})$ suggests the absence of SG phase in the presence of H (at least above 100 Oe). Dynamic scaling analysis of ${\ensuremath{\chi}}^{\ensuremath{''}}(T,\ensuremath{\omega})$ and $\ensuremath{\tau}(T,H)$ near ${T}_{g}$ leads to the critical exponents $(\ensuremath{\beta}=0.36\ifmmode\pm\else\textpm\fi{}0.03,$ $\ensuremath{\gamma}=3.5\ifmmode\pm\else\textpm\fi{}0.4,$ $\ensuremath{\nu}=1.4\ifmmode\pm\else\textpm\fi{}0.2,$ $z=6.6\ifmmode\pm\else\textpm\fi{}1.2,$ $\ensuremath{\psi}=0.24\ifmmode\pm\else\textpm\fi{}0.02,$ and $\ensuremath{\theta}=0.13\ifmmode\pm\else\textpm\fi{}0.02).$ The aging phenomenon is studied through the absorption ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega},t)$ below ${T}_{g}.$ It obeys a $(\ensuremath{\omega}{t)}^{\ensuremath{-}{b}^{\ensuremath{''}}}$ power-law decay with an exponent ${b}^{\ensuremath{''}}\ensuremath{\approx}0.15--0.2.$ The rejuvenation effect is also observed under sufficiently large (temperature and magnetic-field) perturbations.